# Squaring Complex numbers

• May 18th 2009, 05:50 PM
function
Squaring Complex numbers
Hey,

I'm not sure if i'm porting this thread under the right topic, but i just have a quick question about complex numbers.

when you square a complex number (eg. z^2; where z=2+4i) can you just solve this by going z*z???

Thanks,
Function
• May 18th 2009, 05:53 PM
TheEmptySet
Quote:

Originally Posted by function
Hey,

I'm not sure if i'm porting this thread under the right topic, but i just have a quick question about complex numbers.

when you square a complex number (eg. z^2; where z=2+4i) can you just solve this by going z*z???

Thanks,
Function

Yes you can.

$\displaystyle z^2=(2+4i)(2+4i)=4+16i+16i^2=4+16i-16=-12+16i$
• May 19th 2009, 06:26 AM
HallsofIvy
Perhaps function was thinking of |z| which, for a complex number, is $\displaystyle \sqrt{zz*}$ where z* is the complex conjugate of z. For a real number, x, that would be the same as $\displaystyle \sqrt{x^2}$, but not for a non-real complex number.