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

(ii) $z_1-z_2$

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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(ii) z1−z2z_1-z_2

z1−z2=−92+52−92+532i\boxed{z_1-z_2=-\frac{9\sqrt{2}+5}{2}-\frac{9\sqrt{2}+5\sqrt{3}}{2}i}

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