Answer:
(a, b) = (0, -15)
Step-by-step explanation:
In "cis" form the product of two complex numbers is the product of their magnitudes at the angle that is the sum of their angles. I find this the easiest way to multiply complex numbers.
z1 × z2 = (3 cis π)(5 cis π/2)
= (3·5) cis (π +π/2)
= 15 cis 3π/2
Of course, "cis" is short for "cosine + i·sine", so you have ...
z1 × z2 = 15 cis 3π/2 = 15(cos(3π/2) +i·sin(3π/2))
= 15(0 +i·(-1))
= 0 -15i
(a, b) = (0, -15)
