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If z = 3 + 4i, what is the value of z + z̅? (2022)

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Question: If z = 3 + 4i, what is the value of z + z̅? (2022)

Options:

  1. 6
  2. 8
  3. 7
  4. 5

Correct Answer: 8

Solution: 

z + z̅ = (3 + 4i) + (3 - 4i) = 6.

If z = 3 + 4i, what is the value of z + z̅? (2022)

Practice Questions

Q1
If z = 3 + 4i, what is the value of z + z̅? (2022)
  1. 6
  2. 8
  3. 7
  4. 5

Questions & Step-by-Step Solutions

If z = 3 + 4i, what is the value of z + z̅? (2022)
  • Step 1: Identify the given complex number z, which is 3 + 4i.
  • Step 2: Find the conjugate of z, denoted as z̅. The conjugate of a complex number a + bi is a - bi. So, z̅ = 3 - 4i.
  • Step 3: Add z and z̅ together. This means you will add (3 + 4i) and (3 - 4i).
  • Step 4: Combine the real parts: 3 + 3 = 6.
  • Step 5: Combine the imaginary parts: 4i - 4i = 0.
  • Step 6: Write the final result. The sum z + z̅ = 6 + 0i, which simplifies to just 6.
  • Complex Numbers – Understanding the addition of a complex number and its conjugate.
  • Conjugate of a Complex Number – Recognizing that the conjugate of a complex number z = a + bi is z̅ = a - bi.
  • Real and Imaginary Parts – Identifying the real part and the imaginary part of a complex number.
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