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## Homework Statement

What can you say about

a. the sum of a complex number and its conjugate?

b. the conjugate of anumber on the unit circle?

c. the product of two numbers on the unit circle?

d. the sum of two numbers on the unit circle?

## Homework Equations

## The Attempt at a Solution

Here's what I'm thinking:

a. The sum of a complex number and its conjugate is real: (a+bi)+(a-bi)=2a

b. The conjugate of a number on the unit circle LIES ON the unit circle.

c. The product of two numbers on the unit circle also LIES ON the unit circle.

d. The sum of two numbers on the unit circle LIES INSIDE OR OUTSIDE the unit circle.

Am I thinking correctly or am I missing something? I'm unsure on this one. Thanks!