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

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

Options:

  1. 5
  2. 7
  3. 4
  4. 3

Correct Answer: 5

Solution: 

|z| = √(4^2 + (-3)^2) = √(16 + 9) = √25 = 5.

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

Practice Questions

Q1
What is the value of |z| if z = 4 - 3i?
  1. 5
  2. 7
  3. 4
  4. 3

Questions & Step-by-Step Solutions

What is the value of |z| if z = 4 - 3i?
Correct Answer: 5
  • Step 1: Identify the complex number z, which is given as z = 4 - 3i.
  • Step 2: Recognize that |z| represents the magnitude (or absolute value) of the complex number.
  • Step 3: Use the formula for the magnitude of a complex number, which is |z| = √(a^2 + b^2), where a is the real part and b is the imaginary part.
  • Step 4: In our case, the real part a is 4 and the imaginary part b is -3.
  • Step 5: Substitute the values into the formula: |z| = √(4^2 + (-3)^2).
  • Step 6: Calculate 4^2, which is 16.
  • Step 7: Calculate (-3)^2, which is 9.
  • Step 8: Add the results from Step 6 and Step 7: 16 + 9 = 25.
  • Step 9: Take the square root of 25: √25 = 5.
  • Step 10: Conclude that the value of |z| is 5.
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