Manuals/calci/IMEXP

IMEXP(ComplexNumber)

Description

This function gives the exponential of a complex number.
In $IMEXP(ComplexNumber)$ , $ComplexNumber$ is of the form $x+iy$ , $x$ & $y$ are real numbers & $i$ is the imaginary unit. $i={\sqrt {-1}}$ .
Euler's formula states that $e^{ix}=cosx+isinx$ , for any real number $x$ and $e$ is the base of the natural logarithm.
The approximate value of the constant e=2.718281828459045 and it is equal to $e^{1}$ .
Let z be the Complex Number.Then the exponential of a complex number is : $IMEXP(z)=e^{z}=e^{x+iy}=e^{x}.e^{iy}=e^{x}.(cosy+isiny)=e^{x}.cosy+ie^{x}.siny$ .
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 $IMEXP(z)=EXP(z)$ when imaginary number $iy$ 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.