82 Write the complex number in trigonometric form once using

8.2

Write the complex number in trigonometric form, once using degrees and once using radians. Begin by sketching the graph to help find the argument theta. (Do not use cis form.) 3 + 3i degrees radians

Solution

r = sqrt(3^2+(3)^2) = 3sqrt(2)

theta = atan (3/3) = pi/4 rad = 45 degree

Thus in degree =====> 3sqrt(2)*exp(45*i) = 3sqrt(2)(cos 45 +i*sin 45)

And in radian =====> 3sqrt(2)*exp(pi*i/4) = 3sqrt(2)(cos pi/4 +i*sin pi/4)