Theory of Intelligence
11TH•Mathematics•Complex Numbers•Exercise 1.5

Theory

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Theory

  • For z=x+iyz=x+iy:
∣z∣=x2+y2|z|=\sqrt{x^2+y^2}
  • Argument θ\theta is chosen so that:
cos⁡θ=x∣z∣,sin⁡θ=y∣z∣\cos\theta=\frac{x}{|z|},\quad \sin\theta=\frac{y}{|z|}
  • Polar form:
z=∣z∣(cos⁡θ+isin⁡θ)z=|z|(\cos\theta+i\sin\theta)
  • When using tan⁡−1(y/x)\tan^{-1}(y/x), always adjust θ\theta for the correct quadrant.

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