Manuals/calci/IMPOWER

IMPOWER(z,n)

• $z$ is the complex number is of the form $x+iy$
• $n$ is the power value.

Description

• This function gives the value of powers of complex number.
• DeMoivre's Theorem is a generalized formula to compute powers of a complex number in it's polar form.
• i'is the imaginary unit, $i={\sqrt {-1}}$
• Then the power of a complex number is defined by Failed to parse (syntax error): {\displaystyle (z)^n=(x+iy)^n=r^n*e^{inθ}=r^n(cosnθ+isinnθ)} where $r={\sqrt {x^{2}+y^{2}}}$. and Failed to parse (syntax error): {\displaystyle θ=tan^-1(y/x)} , θ∈(-Pi(),Pi()].
• This formula is called DeMoivre's theorem of complex numbers.
• We can use COMPLEX function to convert real and imaginary number in to a complex number.
• In IMPOWER(z,n), n can be integer, fractional or negative.
• suppose n is nonnumeric , this function will returns the error value.

Examples

1. IMPOWER("4+5i",3)=-235.99999+115i
2. IMPOWER("9-7i",4)=-14852-8063.999999i
3. IMPOWER("6",9)=10077696(EXCEL)=10077696-8i(CALCI)
4. IMPOWER("i",10)=-1-16i(CALCI)=-1+6.1257422745431E-16i

See Also

• IMREAL
• IMSUM
• IMAGINARY
• COMPLEX

References

Binary Logarithm