Rectangular Form

Question

Find z₁z₂ and z₁/z₂. Write each answer in rectangular form.

 

z₁=4(cos45°+isin45°), z₂=2(cos15°+isin15°).

 

Please show step by step work to solution and provide final answer. Please and Thank You!

Answer 1

z₁ = 4 cis 45⁰

z₂ = 2 cis 15⁰

 

By DeMoivre's Theorem z₁/z₂ = 2 cis 30^o, i.e. 2(cos 30 + i sin 30), which you may simplify easily.

 

The product of these two z's is 8 cis 60^o