Question

Given a pair of complex numbers, z1 = 5 and z2 = –6i, let z3 = 3i z1 and z4 = z2 – 2. in which quadrant is z3 – z4 located?

Answer 1

Assuming $z_1=5$ and $z_2=-6i$, as well as $z_3=3i z_1$ and $z_4 = z_2-2$, we have

$z_3 - z_4 = 3iz_1 - (z_2-2) = 3i\times5 - (-6i-2) = 15i + 6i + 2 = 2 + 21i$

Since both the real and imaginary parts are positive, $z_3-z_4$ belongs to the first quadrant.