Question

Suppose we multiply a complex number z by 3i.ImDReBOWhich point represents the product of z and 3i?

Answer 1

A complex number can be represented using the exponential form:

$z=re^{i\theta}$

Now, using this notation, we represent 3i:

$3i=3e^{\frac{i\pi}{2}}$

Then, the multiplication of z and 3i:

$3i\cdot z=3e^{\frac{i\pi}{2}}\cdot re^{i\theta}=3re^{i(\theta+\pi/2)}$

Looking at the graph, we must perform a dilation by a factor of 3 and a rotation of π/2 counterclockwise.

The point that best fits these conditions is point B.