Properties from Exponential or Trigonometric form Q6

Properties from Exponential or Trigonometric form Q6

Given that \(z=e^{i\theta}\), find the value of \(\theta\) in radians if \(3+i(3z+1)=e^{i(\pi+\theta)}\) and \(-\pi<\theta<\pi\).

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Answer:\( z = -\frac{3}{5} + \frac{4}{5}i \), \( \arg z \approx 2.21 \) rad\)

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