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What is the modulus of the complex number z = -3 + 4i?

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Question: What is the modulus of the complex number z = -3 + 4i?

Options:

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

Correct Answer: 5

Solution: 

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

What is the modulus of the complex number z = -3 + 4i?

Practice Questions

Q1
What is the modulus of the complex number z = -3 + 4i?
  1. 5
  2. 7
  3. 3
  4. 4

Questions & Step-by-Step Solutions

What is the modulus of the complex number z = -3 + 4i?
Correct Answer: 5
  • Step 1: Identify the complex number z, which is given as z = -3 + 4i.
  • Step 2: Recall that the modulus of a complex number z = a + bi is calculated using the formula |z| = √(a^2 + b^2).
  • Step 3: In our case, a = -3 and b = 4.
  • Step 4: Substitute the values of a and b into the formula: |z| = √((-3)^2 + (4)^2).
  • Step 5: Calculate (-3)^2, which is 9.
  • Step 6: Calculate (4)^2, which is 16.
  • Step 7: Add the results from Step 5 and Step 6: 9 + 16 = 25.
  • Step 8: Take the square root of 25: √25 = 5.
  • Step 9: Therefore, the modulus |z| is 5.
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