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

Solution

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:

Solution

Given:

z1=7(cos⁡23π12+isin⁡23π12),z2=11(cos⁡11π12+isin⁡11π12)z_1=7\left(\cos\frac{23\pi}{12}+i\sin\frac{23\pi}{12}\right),\quad z_2=11\left(\cos\frac{11\pi}{12}+i\sin\frac{11\pi}{12}\right)

First convert to rectangular form.


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