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If z = 1 + i√3, find the argument of z.

Practice Questions

Q1
If z = 1 + i√3, find the argument of z.
  1. π/3
  2. 2π/3
  3. π/6
  4. 5π/6

Questions & Step-by-Step Solutions

If z = 1 + i√3, find the argument of z.
Correct Answer: π/3
  • Step 1: Identify the complex number z, which is given as z = 1 + i√3.
  • Step 2: Recognize that the real part of z is 1 and the imaginary part is √3.
  • Step 3: Use the formula for the argument θ of a complex number, which is θ = tan^(-1)(imaginary part / real part).
  • Step 4: Substitute the values into the formula: θ = tan^(-1)(√3 / 1).
  • Step 5: Simplify the expression: θ = tan^(-1)(√3).
  • Step 6: Recall that tan(π/3) = √3, so θ = π/3.
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