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If z = 2 + 3i, what is the argument of z?

Practice Questions

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

Questions & Step-by-Step Solutions

If z = 2 + 3i, what is the argument of z?
  • Step 1: Identify the complex number z, which is given as z = 2 + 3i.
  • Step 2: Recognize that the argument of a complex number is the angle θ formed with the positive x-axis in the complex plane.
  • Step 3: Use the formula for the argument θ, which is θ = arctan(y/x), where y is the imaginary part and x is the real part of the complex number.
  • Step 4: In this case, the real part (x) is 2 and the imaginary part (y) is 3.
  • Step 5: Substitute the values into the formula: θ = arctan(3/2).
  • Step 6: The result θ = arctan(3/2) gives you the argument of the complex number z.
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