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

(i) $z_1+z_2$

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:

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(i) z1+z2z_1+z_2

z1=−922−922i,z2=52+532iz_1=-\frac{9\sqrt{2}}{2}-\frac{9\sqrt{2}}{2}i,\quad z_2=\frac{5}{2}+\frac{5\sqrt{3}}{2}i z1+z2=5−922+53−922i\boxed{z_1+z_2=\frac{5-9\sqrt{2}}{2}+\frac{5\sqrt{3}-9\sqrt{2}}{2}i}

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