Complex Principal Argument #2

• October 13th 2009, 09:16 PM
Fallen186
Complex Principal Argument #2
$(9+9i)^3$
I tried multipling out the number and then arctan( $\frac{y}{x})$but its not right

I also tried finding the $\theta$ and dividing it by n, "3" ,but it is not the right answer.

it turns out to be $\frac{3\pi}{4}$
• October 13th 2009, 09:18 PM
Chris L T521
Quote:

Originally Posted by Fallen186
$(9+9i)^3$
I tried multipling out the number and then arctan( $\frac{y}{x})$but its not right

I also tried finding the $\theta$ and dividing it by n, "3" ,but it is not the right answer.

it turns out to be $\frac{3\pi}{4}$

Note that $9+9i=9\left(1+i\right)=9e^{i\frac{\pi}{4}}$.

Thus, $z=\left(9+9i\right)^3=9^3e^{i\frac{3\pi}{4}}\impli es\text{Arg}\,z=\frac{3\pi}{4}$

Does this make sense?