Question 1131219
<br>
{{{z = 5+(5*sqrt(3))i}}}<br>
{{{abs(z) = sqrt((5^2)+(5*sqrt(3))^2) = 10}}}
{{{theta = tan^(-1)(5*sqrt(3)/5) = pi/3}}}<br>
{{{z = 10*cis(pi/3)}}}<br>
(Note that, alternatively, you can find the magnitude and the angle by recognizing that the triangle corresponding to the given complex number is a 30-60-90 right triangle with short leg 5.)<br>
{{{z^9= (10*cis(pi/3))^9 = 10^9*cis(9(pi/3)) = 10^9cis(3pi) = -10^9}}}