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What is the value of |z| if z = -1 - i?

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Question: What is the value of |z| if z = -1 - i?

Options:

  1. √2
  2. 2
  3. 1
  4. √3

Correct Answer: √2

Solution: 

The modulus |z| = √((-1)² + (-1)²) = √(1 + 1) = √2.

What is the value of |z| if z = -1 - i?

Practice Questions

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

Questions & Step-by-Step Solutions

What is the value of |z| if z = -1 - i?
  • Step 1: Identify the complex number z. Here, z = -1 - i.
  • Step 2: Recognize that the modulus |z| is calculated using the formula |z| = √(a² + b²), where a is the real part and b is the imaginary part.
  • Step 3: Determine the real part (a) and the imaginary part (b) of z. For z = -1 - i, a = -1 and b = -1.
  • Step 4: Substitute the values of a and b into the formula: |z| = √((-1)² + (-1)²).
  • Step 5: Calculate (-1)², which equals 1. So, |z| = √(1 + 1).
  • Step 6: Add the values inside the square root: 1 + 1 = 2.
  • Step 7: Take the square root of 2: |z| = √2.
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