Squaring Complex numbers

**function** · May 18th 2009, 05:50 PM

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

**TheEmptySet** · May 18th 2009, 05:53 PM

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.

$z^2=(2+4i)(2+4i)=4+16i+16i^2=4+16i-16=-12+16i$

**HallsofIvy** · May 19th 2009, 06:26 AM

Perhaps function was thinking of |z| which, for a complex number, is $\sqrt{zz*}$ where z* is the complex conjugate of z. For a real number, x, that would be the same as $\sqrt{x^2}$ , but not for a non-real complex number.

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