Complex

  • COMPLEX a complex number of the form x + yi
  • IMABS the absolute value of the complex number z
  • IMAGINARY the imaginary part of the complex number z
  • IMARCCOS the complex arccosine of the complex number
  • IMARCCOSH the complex hyperbolic arccosine of the complex number z
  • IMARCCOT the complex arccotangent of the complex number z
  • IMARCCOTH the complex hyperbolic arccotangent of the complex number z
  • IMARCCSC the complex arccosecant of the complex number z
  • IMARCCSCH the complex hyperbolic arccosecant of the complex number z
  • IMARCSEC the complex arcsecant of the complex number z
  • IMARCSECH the complex hyperbolic arcsecant of the complex number z
  • IMARCSIN the complex arcsine of the complex number z
  • IMARCSINH the complex hyperbolic arcsine of the complex number z
  • IMARCTAN the complex arctangent of the complex number
  • IMARCTANH the complex hyperbolic arctangent of the complex number z
  • IMARGUMENT the argument theta of the complex number z
  • IMCONJUGATE the complex conjugate of the complex number z
  • IMCOS the cosine of the complex number z
  • IMCOSH the hyperbolic cosine of the complex number z
  • IMCOT the cotangent of the complex number z
  • IMCOTH the hyperbolic cotangent of the complex number z
  • IMCSC the cosecant of the complex number z
  • IMCSCH the hyperbolic cosecant of the complex number z
  • IMDIV the quotient of two complex numbers z1/z2
  • IMEXP the exponential of the complex number z
  • IMINV the reciprocal, or inverse, of the complex number z
  • IMLN the natural logarithm of the complex number z
  • IMLOG10 the base-10 logarithm of the complex number z
  • IMLOG2 the base-2 logarithm of the complex number z
  • IMNEG the negative of the complex number z
  • IMPOWER the complex number z1 raised to the z2th power
  • IMPRODUCT the product of the given complex numbers
  • IMREAL the real part of the complex number z
  • IMSEC the secant of the complex number z
  • IMSECH the hyperbolic secant of the complex number z
  • IMSIN the sine of the complex number z
  • IMSINH the hyperbolic sine of the complex number z
  • IMSQRT the square root of the complex number z
  • IMSUB the difference of two complex numbers
  • IMSUM the sum of the given complex numbers
  • IMTAN the tangent of the complex number z
  • IMTANH the hyperbolic tangent of the complex number z

COMPLEX

COMPLEX a complex number of the form x + yi

Synopsis

COMPLEX(x,y,i)

Arguments

x: real part

y: imaginary part

i: the suffix for the complex number, either "i" or "j"; defaults to "i"

Note

If i is neither "i" nor "j", COMPLEX returns #VALUE!

Microsoft Excel Compatibility

This function is Excel compatible.

IMABS

IMABS the absolute value of the complex number z

Synopsis

IMABS(z)

Arguments

z: a complex number

Note

If z is not a valid complex number, #VALUE! is returned.

Microsoft Excel Compatibility

This function is Excel compatible.

See also

IMAGINARY, IMREAL.

IMAGINARY

IMAGINARY the imaginary part of the complex number z

Synopsis

IMAGINARY(z)

Arguments

z: a complex number

Note

If z is not a valid complex number, #VALUE! is returned.

Microsoft Excel Compatibility

This function is Excel compatible.

See also

IMREAL.

IMARCCOS

IMARCCOS the complex arccosine of the complex number

Synopsis

IMARCCOS(z)

Arguments

z: a complex number

Description

IMARCCOS returns the complex arccosine of the complex number z. The branch cuts are on the real axis, less than -1 and greater than 1.

Note

If z is not a valid complex number, #VALUE! is returned.

See also

IMARCSIN, IMARCTAN.

IMARCCOSH

IMARCCOSH the complex hyperbolic arccosine of the complex number z

Synopsis

IMARCCOSH(z)

Arguments

z: a complex number

Description

IMARCCOSH returns the complex hyperbolic arccosine of the complex number z. The branch cut is on the real axis, less than 1.

Note

If z is not a valid complex number, #VALUE! is returned.

See also

IMARCSINH, IMARCTANH.

IMARCCOT

IMARCCOT the complex arccotangent of the complex number z

Synopsis

IMARCCOT(z)

Arguments

z: a complex number

Note

If z is not a valid complex number, #VALUE! is returned.

See also

IMARCSEC, IMARCCSC.

IMARCCOTH

IMARCCOTH the complex hyperbolic arccotangent of the complex number z

Synopsis

IMARCCOTH(z)

Arguments

z: a complex number

Note

If z is not a valid complex number, #VALUE! is returned.

See also

IMARCSECH, IMARCCSCH.

IMARCCSC

IMARCCSC the complex arccosecant of the complex number z

Synopsis

IMARCCSC(z)

Arguments

z: a complex number

Note

If z is not a valid complex number, #VALUE! is returned.

See also

IMARCSEC, IMARCCOT.

IMARCCSCH

IMARCCSCH the complex hyperbolic arccosecant of the complex number z

Synopsis

IMARCCSCH(z)

Arguments

z: a complex number

Note

If z is not a valid complex number, #VALUE! is returned.

See also

IMARCSECH, IMARCCOTH.

IMARCSEC

IMARCSEC the complex arcsecant of the complex number z

Synopsis

IMARCSEC(z)

Arguments

z: a complex number

Note

If z is not a valid complex number, #VALUE! is returned.

See also

IMARCCSC, IMARCCOT.

IMARCSECH

IMARCSECH the complex hyperbolic arcsecant of the complex number z

Synopsis

IMARCSECH(z)

Arguments

z: a complex number

Note

If z is not a valid complex number, #VALUE! is returned.

See also

IMARCCSCH, IMARCCOTH.

IMARCSIN

IMARCSIN the complex arcsine of the complex number z

Synopsis

IMARCSIN(z)

Arguments

z: a complex number

Description

IMARCSIN returns the complex arcsine of the complex number z. The branch cuts are on the real axis, less than -1 and greater than 1.

Note

If z is not a valid complex number, #VALUE! is returned.

See also

IMARCCOS, IMARCTAN.

IMARCSINH

IMARCSINH the complex hyperbolic arcsine of the complex number z

Synopsis

IMARCSINH(z)

Arguments

z: a complex number

Description

IMARCSINH returns the complex hyperbolic arcsine of the complex number z. The branch cuts are on the imaginary axis, below -i and above i.

Note

If z is not a valid complex number, #VALUE! is returned.

See also

IMARCCOSH, IMARCTANH.

IMARCTAN

IMARCTAN the complex arctangent of the complex number

Synopsis

IMARCTAN(z)

Arguments

z: a complex number

Description

IMARCTAN returns the complex arctangent of the complex number z. The branch cuts are on the imaginary axis, below -i and above i.

Note

If z is not a valid complex number, #VALUE! is returned.

See also

IMARCSIN, IMARCCOS.

IMARCTANH

IMARCTANH the complex hyperbolic arctangent of the complex number z

Synopsis

IMARCTANH(z)

Arguments

z: a complex number

Description

IMARCTANH returns the complex hyperbolic arctangent of the complex number z. The branch cuts are on the real axis, less than -1 and greater than 1.

Note

If z is not a valid complex number, #VALUE! is returned.

See also

IMARCSINH, IMARCCOSH.

IMARGUMENT

IMARGUMENT the argument theta of the complex number z

Synopsis

IMARGUMENT(z)

Arguments

z: a complex number

Description

The argument theta of a complex number is its angle in radians from the real axis.

Note

If z is not a valid complex number, #VALUE! is returned.

Microsoft Excel Compatibility

This function is Excel compatible.

IMCONJUGATE

IMCONJUGATE the complex conjugate of the complex number z

Synopsis

IMCONJUGATE(z)

Arguments

z: a complex number

Note

If z is not a valid complex number, #VALUE! is returned.

Microsoft Excel Compatibility

This function is Excel compatible.

See also

IMAGINARY, IMREAL.

IMCOS

IMCOS the cosine of the complex number z

Synopsis

IMCOS(z)

Arguments

z: a complex number

Note

If z is not a valid complex number, #VALUE! is returned.

Microsoft Excel Compatibility

This function is Excel compatible.

See also

IMSIN, IMTAN.

IMCOSH

IMCOSH the hyperbolic cosine of the complex number z

Synopsis

IMCOSH(z)

Arguments

z: a complex number

Note

If z is not a valid complex number, #VALUE! is returned.

See also

IMSINH, IMTANH.

IMCOT

IMCOT the cotangent of the complex number z

Synopsis

IMCOT(z)

Arguments

z: a complex number

Description

IMCOT(z) = IMCOS(z)/IMSIN(z).

Note

If z is not a valid complex number, #VALUE! is returned.

See also

IMSEC, IMCSC.

IMCOTH

IMCOTH the hyperbolic cotangent of the complex number z

Synopsis

IMCOTH(z)

Arguments

z: a complex number

Note

If z is not a valid complex number, #VALUE! is returned.

See also

IMSECH, IMCSCH.

IMCSC

IMCSC the cosecant of the complex number z

Synopsis

IMCSC(z)

Arguments

z: a complex number

Description

IMCSC(z) = 1/IMSIN(z).

Note

If z is not a valid complex number, #VALUE! is returned.

See also

IMSEC, IMCOT.

IMCSCH

IMCSCH the hyperbolic cosecant of the complex number z

Synopsis

IMCSCH(z)

Arguments

z: a complex number

Note

If z is not a valid complex number, #VALUE! is returned.

See also

IMSECH, IMCOTH.

IMDIV

IMDIV the quotient of two complex numbers z1/z2

Synopsis

IMDIV(z1,z2)

Arguments

z1: a complex number

z2: a complex number

Note

If z1 or z2 is not a valid complex number, #VALUE! is returned.

Microsoft Excel Compatibility

This function is Excel compatible.

See also

IMPRODUCT.

IMEXP

IMEXP the exponential of the complex number z

Synopsis

IMEXP(z)

Arguments

z: a complex number

Note

If z is not a valid complex number, #VALUE! is returned.

Microsoft Excel Compatibility

This function is Excel compatible.

See also

IMLN.

IMINV

IMINV the reciprocal, or inverse, of the complex number z

Synopsis

IMINV(z)

Arguments

z: a complex number

Note

If z is not a valid complex number, #VALUE! is returned.

IMLN

IMLN the natural logarithm of the complex number z

Synopsis

IMLN(z)

Arguments

z: a complex number

Description

The result will have an imaginary part between -π and +π.

The natural logarithm is not uniquely defined on complex numbers. You may need to add or subtract an even multiple of π to the imaginary part.

Note

If z is not a valid complex number, #VALUE! is returned.

Microsoft Excel Compatibility

This function is Excel compatible.

See also

IMEXP, IMLOG2, IMLOG10.

IMLOG10

IMLOG10 the base-10 logarithm of the complex number z

Synopsis

IMLOG10(z)

Arguments

z: a complex number

Note

If z is not a valid complex number, #VALUE! is returned.

Microsoft Excel Compatibility

This function is Excel compatible.

See also

IMLN, IMLOG2.

IMLOG2

IMLOG2 the base-2 logarithm of the complex number z

Synopsis

IMLOG2(z)

Arguments

z: a complex number

Note

If z is not a valid complex number, #VALUE! is returned.

Microsoft Excel Compatibility

This function is Excel compatible.

See also

IMLN, IMLOG10.

IMNEG

IMNEG the negative of the complex number z

Synopsis

IMNEG(z)

Arguments

z: a complex number

Note

If z is not a valid complex number, #VALUE! is returned.

IMPOWER

IMPOWER the complex number z1 raised to the z2th power

Synopsis

IMPOWER(z1,z2)

Arguments

z1: a complex number

z2: a complex number

Note

If z1 or z2 is not a valid complex number, #VALUE! is returned.

Microsoft Excel Compatibility

This function is Excel compatible.

See also

IMSQRT.

IMPRODUCT

IMPRODUCT the product of the given complex numbers

Synopsis

IMPRODUCT(z1,z2,…)

Arguments

z1: a complex number

z2: a complex number

Note

If any of z1, z2,... is not a valid complex number, #VALUE! is returned.

Microsoft Excel Compatibility

This function is Excel compatible.

See also

IMDIV.

IMREAL

IMREAL the real part of the complex number z

Synopsis

IMREAL(z)

Arguments

z: a complex number

Note

If z is not a valid complex number, #VALUE! is returned.

Microsoft Excel Compatibility

This function is Excel compatible.

See also

IMAGINARY.

IMSEC

IMSEC the secant of the complex number z

Synopsis

IMSEC(z)

Arguments

z: a complex number

Description

IMSEC(z) = 1/IMCOS(z).

Note

If z is not a valid complex number, #VALUE! is returned.

See also

IMCSC, IMCOT.

IMSECH

IMSECH the hyperbolic secant of the complex number z

Synopsis

IMSECH(z)

Arguments

z: a complex number

Note

If z is not a valid complex number, #VALUE! is returned.

See also

IMCSCH, IMCOTH.

IMSIN

IMSIN the sine of the complex number z

Synopsis

IMSIN(z)

Arguments

z: a complex number

Note

If z is not a valid complex number, #VALUE! is returned.

Microsoft Excel Compatibility

This function is Excel compatible.

See also

IMCOS, IMTAN.

IMSINH

IMSINH the hyperbolic sine of the complex number z

Synopsis

IMSINH(z)

Arguments

z: a complex number

Note

If z is not a valid complex number, #VALUE! is returned.

See also

IMCOSH, IMTANH.

IMSQRT

IMSQRT the square root of the complex number z

Synopsis

IMSQRT(z)

Arguments

z: a complex number

Note

If z is not a valid complex number, #VALUE! is returned.

Microsoft Excel Compatibility

This function is Excel compatible.

See also

IMPOWER.

IMSUB

IMSUB the difference of two complex numbers

Synopsis

IMSUB(z1,z2)

Arguments

z1: a complex number

z2: a complex number

Note

If z1 or z2 is not a valid complex number, #VALUE! is returned.

Microsoft Excel Compatibility

This function is Excel compatible.

See also

IMSUM.

IMSUM

IMSUM the sum of the given complex numbers

Synopsis

IMSUM(z1,z2,…)

Arguments

z1: a complex number

z2: a complex number

Note

If any of z1, z2,... is not a valid complex number, #VALUE! is returned.

Microsoft Excel Compatibility

This function is Excel compatible.

See also

IMSUB.

IMTAN

IMTAN the tangent of the complex number z

Synopsis

IMTAN(z)

Arguments

z: a complex number

Note

If z is not a valid complex number, #VALUE! is returned.

Microsoft Excel Compatibility

This function is Excel compatible.

See also

IMSIN, IMCOS.

IMTANH

IMTANH the hyperbolic tangent of the complex number z

Synopsis

IMTANH(z)

Arguments

z: a complex number

Note

If z is not a valid complex number, #VALUE! is returned.

See also

IMSINH, IMCOSH.