Conversion to Polar Form

00:00 4 marks

Convert the complex number \(3 – 4i\) from its rectangular form to polar form. Provide the values of \(r\) and \(\theta\) where \(r\) is the modulus and \(\theta\) is the principal argument in radians and degrees.

Hint Hint

Hint

Recall that the modulus is the distance from the origin, \(r = \sqrt{a^2+b^2}\). For the argument \(\theta = \arctan\left(\frac{b}{a}\right)\), carefully consider the signs of both the real part \(a\) and the imaginary part \(b\) to identify the correct quadrant and adjust \(\theta\) accordingly.

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Answer Answer

Complete Answer

\(r = 5, \theta \approx -53.13^\circ\) or in radians \(\theta \approx -0.93\)

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