For z1 = 5cis 0 and z2 = 7cis π, find z1 · z2 in rectangular form.

Question

Complex Numbers and the Demoivre's Thereom

Answer 1

Hi Luna!

 

z1 times z2 would equal

 

5(cos0 + i sin0) x 7(cos(pi) + i sin(pi))

(5cos0 + 5i sin0)(7cos(pi) + 7i sin(pi)

 

cos 0 = 1

sin 0 =  0

cos pi = -1

sin pi = 0

 

So the last equation becomes

(5(1) + 5i (0)) (7(-1) + 7i (0))

(5 + 0)(-7 + 0)

(5)(-7)

-35

 

Hope this helps!  :)