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If z = 3 + 4i, what is the value of z + z* (where z* is the conjugate of z)? (20

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Question: If z = 3 + 4i, what is the value of z + z* (where z* is the conjugate of z)? (2017)

Options:

  1. 6
  2. 8
  3. 12
  4. 0

Correct Answer: 8

Solution: 

z + z* = (3 + 4i) + (3 - 4i) = 6.

If z = 3 + 4i, what is the value of z + z* (where z* is the conjugate of z)? (20

Practice Questions

Q1
If z = 3 + 4i, what is the value of z + z* (where z* is the conjugate of z)? (2017)
  1. 6
  2. 8
  3. 12
  4. 0

Questions & Step-by-Step Solutions

If z = 3 + 4i, what is the value of z + z* (where z* is the conjugate of z)? (2017)
  • Step 1: Identify the complex number z. Here, z = 3 + 4i.
  • Step 2: Find the conjugate of z, denoted as z*. The conjugate of z = 3 + 4i is z* = 3 - 4i.
  • Step 3: Add z and its conjugate z*. This means we calculate (3 + 4i) + (3 - 4i).
  • Step 4: Combine the real parts and the imaginary parts. The real parts are 3 + 3 = 6, and the imaginary parts are 4i - 4i = 0.
  • Step 5: Write the final result. The sum is 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 changes the sign of the imaginary part.
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