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Q 40 ,ans in English

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ScanSolve AI Answer

Answer

B\text{B}

Step-by-step solution

4 steps

Here's the solution for question 40:

  1. Identify the complex number.

    The complex number is z=−iz = -i.
    In the form x+iyx + iy, we have x=0x = 0 and y=−1y = -1.

  2. Determine the position of the complex number on the complex plane.

    Since the real part x=0x=0 and the imaginary part y=−1y=-1, the complex number −i-i lies on the negative imaginary axis.

  3. Calculate the amplitude (argument).

    For a complex number z=x+iyz = x + iy, the argument arg⁡(z)\arg(z) is the angle it makes with the positive real axis.
    When zz lies on the negative imaginary axis, the angle is −π2-\frac{\pi}{2} (or 3π2\frac{3\pi}{2}). The principal argument is typically in the range (−π,π](-\pi, \pi].
    Therefore, Amp(−i)=−π2\text{Amp}(-i) = -\frac{\pi}{2}.

  4. Match the result with the given options.

    The calculated amplitude is −π2-\frac{\pi}{2}, which corresponds to option (B).

    The final answer is B\text{B}.

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