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If z = 1 + i, find |z|².

Practice Questions

Q1
If z = 1 + i, find |z|².
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Questions & Step-by-Step Solutions

If z = 1 + i, find |z|².
  • Step 1: Identify the complex number z. Here, z = 1 + i.
  • Step 2: Recall the formula for the magnitude squared of a complex number z = a + bi, which is |z|² = a² + b².
  • Step 3: In our case, a = 1 and b = 1 (since i is the imaginary unit and corresponds to 1).
  • Step 4: Substitute the values into the formula: |z|² = (1)² + (1)².
  • Step 5: Calculate (1)², which is 1.
  • Step 6: Calculate (1)² again, which is also 1.
  • Step 7: Add the two results together: 1 + 1 = 2.
  • Step 8: Conclude that |z|² = 2.
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