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

Theory

timer2 min read•forumLesson Discussion

Theory

  • Convert to x+iyx+iy using:
z=r(cos⁡θ+isin⁡θ)=rcos⁡θ+i rsin⁡θz=r(\cos\theta+i\sin\theta)=r\cos\theta+i\,r\sin\theta
  • Multiply/divide in polar form:
z1z2=r1r2(cos⁡(θ1+θ2)+isin⁡(θ1+θ2))z_1z_2=r_1r_2\left(\cos(\theta_1+\theta_2)+i\sin(\theta_1+\theta_2)\right) z1z2=r1r2(cos⁡(θ1−θ2)+isin⁡(θ1−θ2))\frac{z_1}{z_2}=\frac{r_1}{r_2}\left(\cos(\theta_1-\theta_2)+i\sin(\theta_1-\theta_2)\right)
  • Add/subtract after converting to rectangular form.

Discuss theoretical concepts, mathematical formulas, and architectural foundations.

Supports inline code with `backticks`
No comments yet. Be the first to start the discussion!