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NCERT Class XI Mathematics - Complex Numbers and Quadratic Equations - Solutions

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Question : 22 of 52
Marks: +1, -0
i
Solution:  
We have, z = i, i.e., z = 0 + 1⋅i
Let 0 = r cosθ …(i) and 1 = r sinθ …(ii)
Squaring and adding (i) and (ii), we get
r2(cos2θ+sin2θ)r^2(\cos^2 \theta + \sin^2 \theta) = 1 ⇒ r2r^2 = 1 ⇒ r = 1
∴ cosθ = 0, sinθ = 1
⇒ cos θ = cos π2\frac{\pi}{2} , sin θ = sin π2\frac{\pi}{2}
Here, cos θ = 0 and sin θ > 0
∴ θ lies in first quadrant.
∴ θ = π2\frac{\pi}{2}
∴ The required polar form is z = 1 (cosπ2+isinπ2)\left( \cos \frac{\pi}{2} + i \sin \frac{\pi}{2} \right)
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