Complex Principal Argument #2

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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?

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