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

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

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

z1z2=711(cos⁡π+isin⁡π)=711(−1+0i)\frac{z_1}{z_2}=\frac{7}{11}(\cos\pi+i\sin\pi)=\frac{7}{11}(-1+0i) z1z2=−711+0i\boxed{\frac{z_1}{z_2}=-\frac{7}{11}+0i}

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