Manuals/calci/IMEXP

IMEXP(z)

• where $z$ is the complex number.

Description

• This function gives the exponential of a complex number.
• In $IMEXP(z)$, $z$ is the complex number of the form $z=x+iy$, $x$&$y$ 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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle e^1} . So the exponential of a complex number is : Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle IMEXP(z) = e^z = e^{x+iy} = e^{x}.e^{iy} = e^{x}.(cosy+isiny)=e^x.cosy+ie^x.siny} .
• 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'.
• We can use COMPLEX function to convert the real and imaginary coefficients to a complex number.

Examples

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

See Also

• COMPLEX
• IMAGINARY
• IMREAL
• EXP

References

Exponential function