fin the product z1 * z2 and quotient z1/z2 using the standard form for z1 and z2.

Question

z1 = 2 - 3i and z2 = 1 - sqrt 3i

Answer 1

Z1 = 2-3i, Z2 = 1-sqrt(3)i.

Z1*Z2 = (2-3i)(1-sqrt(3)i),
= 2-2sqrt(3)i-3i+3sqrt(3)*-1,
= 2-6.46i-5.2,

Z1*Z2 = -3.2 - 6.46i

Or
Convert both to polar form and get:
Z1*Z2 = (3.61,-56.3deg)(2,-60deg),

Z1*Z2=(7.22,-116.3deg) = -3.2 - 6.47i.

Z1/Z2 = (3.61,-56.3deg)/(2,-60deg),
Z1/Z2 = (1.8,3.7deg) = 1.796 - 0.1162i.