The question:

Evaluate $\displaystyle (2 + 3i)^3$

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!

Printable View

- Feb 28th 2011, 09:23 PMGlitchMind blank: Powers of complex numbers
**The question:**

Evaluate $\displaystyle (2 + 3i)^3$

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! - Feb 28th 2011, 11:11 PMlanierms
I don't know what polar form is. I think the best way to do it is just doing it.

Solution:

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

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

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

$\displaystyle =-46+9i$ - Mar 1st 2011, 12:12 AMGlitch
Fair enough, I guess I should do things the easy way. :P

Thanks!