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If z = a + bi, what is the conjugate of z?

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Question: If z = a + bi, what is the conjugate of z?

Options:

  1. a - bi
  2. a + bi
  3. -a + bi
  4. -a - bi

Correct Answer: a - bi

Solution: 

The conjugate of z = a + bi is z̅ = a - bi.

If z = a + bi, what is the conjugate of z?

Practice Questions

Q1
If z = a + bi, what is the conjugate of z?
  1. a - bi
  2. a + bi
  3. -a + bi
  4. -a - bi

Questions & Step-by-Step Solutions

If z = a + bi, what is the conjugate of z?
  • Step 1: Identify the complex number z, which is given as z = a + bi.
  • Step 2: Recognize that 'a' is the real part and 'bi' is the imaginary part of the complex number.
  • Step 3: To find the conjugate of z, you need to change the sign of the imaginary part.
  • Step 4: The imaginary part 'bi' becomes '-bi' when you take the conjugate.
  • Step 5: Write the conjugate of z as z̅ = a - bi.
  • Complex Numbers – Understanding the representation of complex numbers in the form z = a + bi, where a is the real part and bi is the imaginary part.
  • Complex Conjugate – The concept of the complex conjugate, which involves changing the sign of the imaginary part of a complex number.
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