Find the product z1 z2 and the quotient z1z2 Express your an

Find the product z_1 z_2 and the quotient z_1/z_2. Express your answers in polar form. z_1 = squareroot 2(cos (80 degree) + i sin (80 degree)), z_2 = 4 squareroot 2 (cos (65 degree) + I sin (65 degree))

Solution

In polar form we can write z1 = re^ix

where r= mangnitude ; x= angle

z1 = sqrt(2)e^(i80)

Similarly z2 = 4sqrt2e^(i65)

z1z2 = 8e^i(145) =

Similarly z1/z2 = sqrt2e^i80/ 4sqrt2e^i65

= e^i(80-65) / 4

= 0.25e^i15