Number and algebraCourse skill

Dividing complex numbers using a conjugate

Multiply by the conjugate of the denominator to make it real.

  • The conjugate of is .
  • Multiply the numerator and denominator by that same conjugate.
  • Use , then simplify.

Example 1

Make the denominator real

Simplify the expression.

Example 2

Fully simplify the expression.

Your turn

5 practice questions
Question 1

Simplify.

Check answer
Multiply by the conjugate of the denominator.
Question 2

Simplify.

Check answer
Multiply by the conjugate of the denominator.
Question 3

Simplify.

Check answer
Multiply by the conjugate of the denominator.
Question 4

Simplify.

Check answer
Multiply by the conjugate of the denominator.
Question 5

Simplify.

Check answer
Multiply by the conjugate of the denominator.
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