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If z = 1 + i, what is the argument of z?

Practice Questions

Q1
If z = 1 + i, what is the argument of z?
  1. π/4
  2. π/2
  3. 0
  4. π

Questions & Step-by-Step Solutions

If z = 1 + i, what is the argument of z?
  • Step 1: Identify the complex number z. Here, z = 1 + i.
  • Step 2: Recognize that in the complex number z = a + bi, 'a' is the real part and 'b' is the imaginary part. For z = 1 + i, a = 1 and b = 1.
  • Step 3: Use the formula for the argument of a complex number, which is θ = tan⁻¹(b/a).
  • Step 4: Substitute the values of a and b into the formula: θ = tan⁻¹(1/1).
  • Step 5: Calculate tan⁻¹(1/1), which equals tan⁻¹(1).
  • Step 6: Recognize that tan⁻¹(1) corresponds to an angle of π/4 radians.
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