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Find the conjugate of the complex number z = 5 - 6i.

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Question: Find the conjugate of the complex number z = 5 - 6i.

Options:

  1. 5 + 6i
  2. 5 - 6i
  3. -5 + 6i
  4. -5 - 6i

Correct Answer: 5 + 6i

Solution: 

The conjugate of z = 5 - 6i is z̅ = 5 + 6i.

Find the conjugate of the complex number z = 5 - 6i.

Practice Questions

Q1
Find the conjugate of the complex number z = 5 - 6i.
  1. 5 + 6i
  2. 5 - 6i
  3. -5 + 6i
  4. -5 - 6i

Questions & Step-by-Step Solutions

Find the conjugate of the complex number z = 5 - 6i.
Correct Answer: z̅ = 5 + 6i
  • Step 1: Identify the complex number z. In this case, z = 5 - 6i.
  • Step 2: Understand that the conjugate of a complex number is found by changing the sign of the imaginary part.
  • Step 3: The imaginary part of z is -6i. To find the conjugate, change -6i to +6i.
  • Step 4: Write the conjugate of z. The conjugate is z̅ = 5 + 6i.
  • Complex Conjugate – The complex conjugate of a complex number is obtained by changing the sign of the imaginary part.
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