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If z = -2 + 2i, what is the value of |z|? (2019)

Practice Questions

Q1
If z = -2 + 2i, what is the value of |z|? (2019)
  1. 2√2
  2. 4
  3. 2
  4. √2

Questions & Step-by-Step Solutions

If z = -2 + 2i, what is the value of |z|? (2019)
  • Step 1: Identify the complex number z. Here, z = -2 + 2i.
  • Step 2: Recall the formula for the magnitude (or absolute value) of a complex number z = a + bi, which is |z| = √(a^2 + b^2).
  • Step 3: In our case, a = -2 and b = 2.
  • Step 4: Substitute a and b into the formula: |z| = √((-2)^2 + (2)^2).
  • Step 5: Calculate (-2)^2, which is 4.
  • Step 6: Calculate (2)^2, which is also 4.
  • Step 7: Add the results from Step 5 and Step 6: 4 + 4 = 8.
  • Step 8: Take the square root of 8: |z| = √8.
  • Step 9: Simplify √8 to 2√2.
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