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What is the conjugate of the complex number z = 2 + 5i?

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Question: What is the conjugate of the complex number z = 2 + 5i?

Options:

  1. 2 - 5i
  2. 2 + 5i
  3. -2 + 5i
  4. -2 - 5i

Correct Answer: 2 - 5i

Solution: 

The conjugate of z = 2 + 5i is z̅ = 2 - 5i.

What is the conjugate of the complex number z = 2 + 5i?

Practice Questions

Q1
What is the conjugate of the complex number z = 2 + 5i?
  1. 2 - 5i
  2. 2 + 5i
  3. -2 + 5i
  4. -2 - 5i

Questions & Step-by-Step Solutions

What is the conjugate of the complex number z = 2 + 5i?
Correct Answer: z̅ = 2 - 5i
  • Step 1: Identify the complex number. In this case, the complex number is z = 2 + 5i.
  • 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 is 5i. To find the conjugate, we change 5i to -5i.
  • Step 4: Write the conjugate using the real part and the new imaginary part. The real part is 2, and the new imaginary part is -5i.
  • Step 5: Combine them to get the conjugate: z̅ = 2 - 5i.
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