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If z = 1 + i, find the conjugate of z.

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Question: If z = 1 + i, find the conjugate of z.

Options:

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

Correct Answer: 1 - i

Solution: 

The conjugate of z = 1 + i is z̅ = 1 - i.

If z = 1 + i, find the conjugate of z.

Practice Questions

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

Questions & Step-by-Step Solutions

If z = 1 + i, find the conjugate of z.
  • Step 1: Identify the complex number z. In this case, z = 1 + i.
  • 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 = 1 + i is +i. To find the conjugate, we change +i to -i.
  • Step 4: Write the conjugate of z. So, the conjugate z̅ = 1 - i.
  • Complex Numbers – Understanding the representation of complex numbers and their conjugates.
  • Conjugate of a Complex Number – The conjugate of a complex number is obtained by changing the sign of the imaginary part.
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