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MHT CET202523 Apr 2025Evening ShiftMathematicsComplex NumberActual

Argument of the complex number z = 13-5 i 4-9 i , i= -1 is

Options

  1. A4
  2. B2
  3. C6
  4. D3

Correct answer

A. 4

Step-by-step solution

The complex number z = 13 - 5i 4 - 9i is simplified by multiplying numerator and denominator by the conjugate of the denominator, 4 + 9i . For the numerator: (13 - 5i)(4 + 9i) = 52 + 117i - 20i - 45i^2 = 52 + 97i + 45 = 97 + 97i The denominator simplifies to: (4 - 9i)(4 + 9i) = 16 + 81 = 97 Thus, z = 97 + 97i 97 = 1 + i The argument is given by = Im (z) Re (z) = 1 1 = 1 . Since z lies in the first quadrant, the principal argument is = 4 . Final answer: 4

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