Perform the indicated operations for the resulting complex numbers if the given changes are made in the indicated examples of this section.

In Example 4, change the exponent to 5 and then find the result.

Data from Example 4

Using DeMoivre’s theorem, find (2 + 3 j)³. Converting to polar form, 2 + 3j = 3.61∠56.3°. Therefore 

Expressing θ in radians, we have θ = 56.3° = 0.983 rad. Therefore,

[3.61(cos 56.3 + j sin 56.3)] = (3.61) [cos(3 x 56.3) + jsin(3 x 56.3)] = 47.0 (cos 168.9 + j sin 168.9) = 47.0/168.9