Question

Find the product of z1 and z2 where z1 = 2(cos 80° + i sin 80°), and z2 = 9(cos 110° + i sin 110°).

11(cos 190° + i sin 190°)
18(cos 8800° + i sin 8800°)
18(cos 190° + i sin 190°)
18(cos 80° + i sin 80°)

Answer 1

Rule:
If
\[\Large z_1 = \color{red}{r_1}*\left(\cos(\color{blue}{\theta_1})+i*\sin(\color{blue}{\theta_1})\right)\]
\[\Large z_2 = \color{green}{r_2}*\left(\cos(\color{orange}{\theta_2})+i*\sin(\color{orange}{\theta_2})\right)\]
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Then
\[\Large z_1*z_2 = \color{red}{r_1}*\color{green}{r_2}*\left(\cos(\color{blue}{\theta_1}+\color{orange}{\theta_2})+i*\sin(\color{blue}{\theta_1}+\color{orange}{\theta_2})\right)\]