Theory of Intelligence
11TH•Mathematics•Complex Numbers•Question 2

Solution

Express the following complex numbers in polar form:

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Solution

For z=x+iyz=x+iy:

r=∣z∣=x2+y2,θ=tan⁡−1(yx) (adjust quadrant)r=|z|=\sqrt{x^2+y^2},\quad \theta=\tan^{-1}\left(\frac{y}{x}\right)\ \text{(adjust quadrant)}

and

z=r(cos⁡θ+isin⁡θ)z=r(\cos\theta+i\sin\theta)

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