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 + 3 i

Solution

3+3i

z=sqrt(3² +3²)=3sqrt2

tan theta= y/x

tan theta= 3/3=1

theta= tan^-11=45 degree

required trigonometri form in degree is

3sqrt2 ( cos45 + i sin45)

and in radian is

3sqrt2 ( cos pi/4 + i sin pi/4)