# Manuals/calci/IMEXP

IMEXP(ComplexNumber)

• is of the form x+iy.
• IMEXP(), returns the exponential of a complex number.

## Description

• This function gives the exponential of a complex number.
• In , is of the form , & are real numbers & is the imaginary unit. .
• Euler's formula states that , for any real number and is the base of the natural logarithm.
• The approximate value of the constant e=2.718281828459045 and it is equal to .
• Let z be the Complex Number.Then the exponential of a complex number is : .
• Here Sin and Cos are trignometric functions. y is angle value in radians.
• When imaginary part is '0', it will give the exponent value of the real number. i.e when imaginary number is '0'.
• The Complex exponential function is denoted by "cis(x)"(Cosine plus iSine)
• We can use COMPLEX function to convert the real and imaginary coefficients to a complex number.

## ZOS

• The syntax is to calculate IMEXP in ZOS is .
• is of the form a+bi.
• For e.g.,IMEXP("0.3-0.54i")
IMEXP

## Examples

1. =IMEXP("2+3i") = -7.315110094901102+1.0427436562359i
2. =IMEXP("4-5i") = 15.4874305606508+52.355491418482i
3. =IMEXP("6") = 403.428793492735+0i
4. =IMEXP("2i") = -0.416146836547142+0.909297426825682i
5. =IMEXP("0") = 1+0i and IMEXP("0i") = 1+0i

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