Find zw or zw as specified Leave your answer in polar form z

Find zw or z/w as specified. Leave your answer in polar form. z = 10(cos 30degree + i sin 30 degree) w = 5(cos 10degree + i sin 10degree) Find zw.

Solution

z=10(cos30 + i sin 30)

w= 5(cos 10 + i sin 10)  

First we have to convert degrees to radians

30 degree= .523599 radians

10 degrees=.174533 radians

Now we have to convert each of them to exponential form in the following manner

r(cos theta + i sin theta) = r e^{i theta}

Therefore 10(cos .523599 + i sin .523599) = 10e^{.523599 i}

                  5(cos.174533 + i sin .174533)   = 5e^.174533i

10e^{.523599 i} * 5 e^{.174533 i} = 50 e^{i(.523599 +.174533)} = 50e^{.698132 i}

Now we have to convert .698132 radians to degree

.698132 radians=40 degree

Therefore z.w=50(cos 40 + i sin 40)