# Worksheet: Complex Number Conjugates

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

Q1:

Find the complex conjugate of and the sum of this number with its complex conjugate.

• A,
• B,
• C, 0
• D,

Q2:

Is it true that for all ?

• Ayes
• Bno

Q3:

What is the conjugate of the complex number ?

• A
• B
• C
• D
• E

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

Q14:

Find the complex conjugate of and the product of this number with its complex conjugate.

• A, 1
• B, 0
• C, 2
• D, 0

Q15:

If , what is ?

Q16:

Given that , determine the value of .

Q17:

Given that and , determine the value of .

Q18:

Given that , determine the value of .

Q19:

Solve in .

• A
• B
• C
• D

Q20:

Simplify .

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,

Q23:

Solve .

• 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