Question

In the graph, z is a complex number represented as a vector from the origin. What is the product of z and its conjugate?

Answer 1

The blue dot? Or the other one

Answer 2

Answer:

5

Step-by-step explanation:

Given a complex number x + yi then the conjugate is x - yi

Note the real part remains unchanged while the sign of the imaginary part is negated.

here z = 1 - 2i hence conjugate is 1 + 2i

and the product is

(1 - 2i)(1 + 2i) ← expand factors

= 1 - 4i² [ i² = - 1 ]

= 1 + 4

= 5