# Worksheet: Complex Number Conjugates

In this worksheet, we will practice using the properties of conjugate numbers to evaluate an expression.

**Q2: **

Is it true that for all ?

- Ayes
- Bno

**Q4: **

What is the conjugate of the complex number ?

- A
- B
- C
- D
- E

**Q5: **

How do you find the conjugate of a complex number?

- AChange the sign of both the real and imaginary parts.
- BSwap the real and imaginary parts.
- CChange the sign of its imaginary part.
- DSwap the real and imaginary parts, then change the sign of them both.
- EChange the sign of its real part.

**Q6: **

Is the complex conjugate of the number ?

- Ano
- Byes

**Q7: **

If ,what is ?

- A
- B
- C
- D
- E8

**Q8: **

Is the complex conjugate of the number ?

- Ano
- Byes

**Q9: **

Is the sum of a number and its complex conjugate always a real number?

- Ayes
- Bno

**Q10: **

Is the product of a number and its complex conjugate always a real number?

- Ayes
- Bno

**Q11: **

If is a real number, what will its conjugate be equal to?

- A
- B
- C
- D

**Q12: **

Is it true that for all ?

- AYes
- BNo

**Q13: **

Is it true that for all ?

- AYes
- BNo

**Q15: **

If , what is ?

**Q16: **

Given that , determine the value of .

**Q18: **

Given that , determine the value of .

**Q19: **

Solve in .

**Q21: **

Simplify .

- A
- B
- C0
- D
- E

**Q22: **

Consider and .

Calculate and .

- A ,
- B ,
- C ,
- D ,
- E ,

Find and .

- A ,
- B ,
- C ,
- D ,
- E ,

Find and .

- A ,
- B ,
- C ,
- D ,
- E ,

**Q24: **

Given that and , express the complex conjugate of in the form .

- A
- B
- C
- D
- E

**Q25: **

If and , find .

- A
- B
- C
- D
- E