Theory of Intelligence
11TH•Mathematics•Complex Numbers•Question 5

(ii) $z_1-z_2$

If $z_1=7\left(\cos\dfrac{23\pi}{12}+i\sin\dfrac{23\pi}{12}\right)$ and $z_2=11\left(\cos\dfrac{11\pi}{12}+i\sin\dfrac{11\pi}{12}\right)$ then find the following and express the result into $x+iy$ form:

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(ii) z1−z2z_1-z_2

z1−z2=9(6+2)2−9(6−2)2i\boxed{z_1-z_2=\frac{9(\sqrt{6}+\sqrt{2})}{2}-\frac{9(\sqrt{6}-\sqrt{2})}{2}i}

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