Question

Which phrase describes the geometric interpretation of dividing a complex number z by i?
O Reflect z across the real axis.
O Reflect z across the imaginary axis.
O Rotate z by 90° clockwise about the origin.
O Rotate z by 90° counterclockwise about the origin.

Answer 1

Answer:  Rotate z by 90° clockwise about the origin.

Step-by-step explanation:

Suppose we have the number z = a + b*i, that can be represented with the point (a, b) in a coordinate axis.

If we divide z by i, we have:

$\frac{z}{i} = \frac{a + b*i}{i} = \frac{a + b*i}{i} *\frac{i}{i} = \frac{a*i - b}{-1} = b - a*i$

This point will be represented with the point (b, -a)

Then we have the transformation:

(a, b) ----> (b, -a)

This is a rotation of 90° clockwise about the origin.

Then the correct option is:

Rotate z by 90° clockwise about the origin.

Answer 2

Answer:

C

Step-by-step explanation:

rotate Z clockwize