Question

Find the product of z1 and z2 where z1 = 7(cos 40° + i sin 40°), and z2 = 6(cos 145° + i sin 145°).

Answer 1

Use the law of De Moivre.

Answer 2

Which means that scalar identities will get multiplied and angular/phase identities will get added.

Answer 3

@Spacelimbus how do I set that up?

Answer 4

Do you see the angles within the cos identities? When you multiply two complex numbers in polar form, these two angular identities just get added together.

Answer 5

@Spacelimbus no

Answer 6

just look at the cos(40°) and cos(145°) for now, what happens if you add these two angles together?

Answer 7

@Spacelimbus i get -0.0532

Answer 8

the first identities should be cos(40++145°)=cos(185°) now do the same with the sin.

Answer 9

@spacelimbus 2sin185

Answer 10

not 2 sin, just add the angles together. but the angle is right.

Answer 11

so far you're at:
(cos(185°)+isin(185°)) now all there is left to do is multiplying the factors in front

Answer 12

@Spacelimbus 42(cos185+isin185) ?

Answer 13

exactly