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

Solution

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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Solution

Given:

z1=9(cos⁡5π4+isin⁡5π4),z2=5(cos⁡π3+isin⁡π3)z_1=9\left(\cos\frac{5\pi}{4}+i\sin\frac{5\pi}{4}\right),\quad z_2=5\left(\cos\frac{\pi}{3}+i\sin\frac{\pi}{3}\right)

Convert to rectangular form when adding/subtracting, and use polar rules for multiplication/division.

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