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MHT CET202611 April 2026Morning ShiftMathematicsComplex NumberActual

If -1 + -3 = r e^ i , then the value of is

Options

  1. A- 2 3
  2. B3
  3. C- 3
  4. D2 3

Correct answer

D. 2 3

Step-by-step solution

Given complex number is z = -1 + -3 = -1 + i 3 . Let z = r e^ i , where r = |z| and = (z) . The real part x = -1 and the imaginary part y = 3 . Since x 0 , the complex number lies in the second quadrant. The principal argument is given by - ⁻¹ ( | y x | ) . = - ⁻¹( 3 ) = - 3 = 2 3 . Answer: 2 3

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