Theory of Intelligence
11TH•Mathematics•Complex Numbers•Question 2

(i) $4+3i$

Express the following complex numbers in polar form:

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(i) 4+3i4+3i

r=∣z∣=42+32=5 r=|z|=\sqrt{4^2+3^2}=5

Since x>0x>0 and y>0y>0, θ\theta lies in Quadrant I:

θ=tan⁡−1(34)\theta=\tan^{-1}\left(\frac{3}{4}\right) 4+3i=5(cos⁡(tan⁡−134)+isin⁡(tan⁡−134))\boxed{4+3i=5\left(\cos\left(\tan^{-1}\frac{3}{4}\right)+i\sin\left(\tan^{-1}\frac{3}{4}\right)\right)}

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