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What is the value of |z|^2 if z = 4 - 3i?

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Question: What is the value of |z|^2 if z = 4 - 3i?

Options:

  1. 25
  2. 16
  3. 7
  4. 12

Correct Answer: 25

Solution: 

|z|^2 = 4^2 + (-3)^2 = 16 + 9 = 25.

What is the value of |z|^2 if z = 4 - 3i?

Practice Questions

Q1
What is the value of |z|^2 if z = 4 - 3i?
  1. 25
  2. 16
  3. 7
  4. 12

Questions & Step-by-Step Solutions

What is the value of |z|^2 if z = 4 - 3i?
Correct Answer: 25
  • Step 1: Identify the complex number z. Here, z = 4 - 3i.
  • Step 2: Recall that the magnitude squared of a complex number z = a + bi is given by |z|^2 = a^2 + b^2.
  • Step 3: In our case, a = 4 and b = -3.
  • Step 4: Calculate a^2. This is 4^2 = 16.
  • Step 5: Calculate b^2. This is (-3)^2 = 9.
  • Step 6: Add the results from Step 4 and Step 5. So, 16 + 9 = 25.
  • Step 7: Conclude that |z|^2 = 25.
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