Question

please help!! medal & fan

z1=8(cos 2pi/3 + isin 2pi/3)
z2= 0.5(cos pi/3 + isin pi/3)

write the rectangular form of z1z2.

Answer 1

@perl @Michele_Laino

Answer 2

@paki @sammixboo

Answer 3

@iambatman @EclipsedStar

Answer 4

@ElonaSushchik

Answer 5

@geerky42

Answer 6

1. z1/z2 = 8 (cos π/3 + i sin π/3) = 8 (1/2 + i √3/2) = 4 + 4i √2

Answer 7

is that z1? @ElonaSushchik

Answer 8

ya

Answer 9

so then how do i multiply that with z2? cause i have to multiply z1 and z2 @ElonaSushchik

Answer 10

@owllover123 help me pls!!

Answer 11

For two complex numbers \(\large z_1=re^{i\theta}\) and \(\large z_2=se^{i\phi}\) (where \(\large e^{i\theta}=\cos\theta+i\sin\theta\)), you have
\[\large z_1z_2=rse^{i(\theta+\phi)}\]
All this means is that you multiply the moduli \(r\) and \(s\), and add the arguments \(\theta\) and \(\phi\).

So what's \(8\times0.5\)? What's \(\dfrac{2\pi}{3}+\dfrac{\pi}{3}\)?

Answer 12

@perl @izzy529 @sammixboo