Question

Find the product of z1 and z2 where z1 = 8(cos 40° + i sin 40°), and z2 = 4(cos 135° + i sin 135°).

Answer 1

\[e^{i \theta}=\cos(\theta)+i \sin(\theta)\]

Answer 2

???

Answer 3

if z1 = r1*[cos(theta1) + i*sin(theta1)] and z2 = r2*[cos(theta2) + i*sin(theta2)]

then

z1*z2 = (r1*r2)*[cos(theta1+theta2) + i*sin(theta1+theta2)]

Answer 4

Can you send a drawing?

Answer 5

Use the draw tool.

Answer 6

?

Answer 7

if

\[\Large z_1 = r_1[\cos(\theta_1)+i*\sin(\theta_1)]\]

and

\[\Large z_2 = r_2[\cos(\theta_2)+i*\sin(\theta_2)]\]

Answer 8

then

\[\Large z_1*z_2 = (r_1*r_2)[\cos(\theta_1+\theta_2)+i*\sin(\theta_1+\theta_2)]\]

Answer 9

Oh, okay.

Answer 10

What would it look like with the numbers plugged in?

Answer 11

in this case,

r1 = 8, r2 = 4

theta1 = 40, theta2 = 135

Answer 12

Thanks.