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If z = 5 + 12i, what is the argument of z? (2022)

Practice Questions

Q1
If z = 5 + 12i, what is the argument of z? (2022)
  1. arctan(12/5)
  2. arctan(5/12)
  3. π/2
  4. 0

Questions & Step-by-Step Solutions

If z = 5 + 12i, what is the argument of z? (2022)
  • Step 1: Identify the complex number z, which is given as z = 5 + 12i.
  • Step 2: Recognize that the argument of a complex number is the angle it makes with the positive x-axis in the complex plane.
  • Step 3: Use the formula for the argument, which is arctan(y/x), where y is the imaginary part and x is the real part.
  • Step 4: In this case, the real part (x) is 5 and the imaginary part (y) is 12.
  • Step 5: Substitute the values into the formula: arctan(12/5).
  • Step 6: Calculate the value of arctan(12/5) to find the argument of z.
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