Manuals/calci/IMEXP

IMEXP(ComplexNumber)

• $ComplexNumber$ 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 $IMEXP(ComplexNumber)$, $ComplexNumber$ 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.

ZOS

• The syntax is to calculate IMEXP in ZOS is $IMEXP(ComplexNumber)$.
  • $ComplexNumber$ 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

Related Videos

Exponential Form of Complex Number

See Also

• COMPLEX
• IMAGINARY
• IMREAL
• EXP

References

Exponential function

• List of Main Z Functions

• Z3 home