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If z = 2 + 2i, find the conjugate of z.

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Question: If z = 2 + 2i, find the conjugate of z.

Options:

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

Correct Answer: 2 - 2i

Solution: 

The conjugate of z = 2 + 2i is z̅ = 2 - 2i.

If z = 2 + 2i, find the conjugate of z.

Practice Questions

Q1
If z = 2 + 2i, find the conjugate of z.
  1. 2 - 2i
  2. 2 + 2i
  3. -2 + 2i
  4. -2 - 2i

Questions & Step-by-Step Solutions

If z = 2 + 2i, find the conjugate of z.
Correct Answer: z̅ = 2 - 2i
  • Step 1: Identify the complex number z. In this case, z = 2 + 2i.
  • Step 2: Understand that the conjugate of a complex number is found by changing the sign of the imaginary part. The imaginary part here is +2i.
  • Step 3: Change the sign of the imaginary part. So, +2i becomes -2i.
  • Step 4: Write the conjugate of z using the real part and the new imaginary part. The conjugate is z̅ = 2 - 2i.
  • Complex Conjugate – The conjugate of a complex number is obtained by changing the sign of the imaginary part.
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