Properties from Exponential or Trigonometric form Q5

Properties from Exponential or Trigonometric form Q5

Find the modulus and argument of \({{\left( \frac{3-i}{1-2i} \right)}^{22}}\) in exact form and hence write the complex number in the exponential form.

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Answer:\( 2^{11} e^{-i\frac{\pi}{2}} \) or \( -2048i \)

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