Theory of Intelligence
11TH•Mathematics•Complex Numbers•Question 4

(iv) $\dfrac{z_1}{z_2}$

If $z_1=9\left(\cos\dfrac{5\pi}{4}+i\sin\dfrac{5\pi}{4}\right)$ and $z_2=5\left(\cos\dfrac{\pi}{3}+i\sin\dfrac{\pi}{3}\right)$ then find:

timer2 min read•forumLesson Discussion

(iv) z1z2\dfrac{z_1}{z_2}

z1z2=95(cos⁡11π12+isin⁡11π12)\frac{z_1}{z_2}=\frac{9}{5}\left(\cos\frac{11\pi}{12}+i\sin\frac{11\pi}{12}\right) cos⁡11π12=−6+24,sin⁡11π12=6−24\cos\frac{11\pi}{12}=-\frac{\sqrt{6}+\sqrt{2}}{4},\quad \sin\frac{11\pi}{12}=\frac{\sqrt{6}-\sqrt{2}}{4} z1z2=−9(6+2)20+9(6−2)20i\boxed{\frac{z_1}{z_2}=-\frac{9(\sqrt{6}+\sqrt{2})}{20}+\frac{9(\sqrt{6}-\sqrt{2})}{20}i}

Discuss theoretical concepts, mathematical formulas, and architectural foundations.

Supports inline code with `backticks`
No comments yet. Be the first to start the discussion!
arrow_back
Previous Part
(iii)