# Mind blank: Powers of complex numbers

• February 28th 2011, 10:23 PM
Glitch
Mind blank: Powers of complex numbers
The question:
Evaluate $(2 + 3i)^3$

If I remember correctly, the best way to do this is to convert to polar form, then apply the power. However, I'm getting crazy answers like 2035 - 828.02i

Any assistance would be great!
• March 1st 2011, 12:11 AM
lanierms
I don't know what polar form is. I think the best way to do it is just doing it.

Solution:

$(2+3i)^2(2+3i)$

$=(-5+12i)(2+3i)$

$=-10-15i+24i-36$

$=-46+9i$
• March 1st 2011, 01:12 AM
Glitch
Fair enough, I guess I should do things the easy way. :P

Thanks!