Question

1. Given z_1=5(cos⁡〖20°〗+i sin⁡〖20°〗 ),z_2=4(cos⁡〖10°〗+i sin⁡〖10°〗) find: (Leave answer in polar form.)

z_1^5

Answer 1

By DeMoivre's theorem, you have


`z_1=5(\cos20^\circ+i\sin20^\circ)`

`\implies {z_1}^5=5^5(\cos100^\circ+i\sin100^\circ)`