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NCERT Class XI Mathematics - Complex Numbers and Quadratic Equations - Solutions
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Question : 20 of 52
Marks:
+1,
-0
– 3
Solution:
We have, z = –3, i.e., z = –3 + 0i Let –3 = r cosθ …(i) and 0 = r sinθ …(ii) Squaring and adding (i) and (ii), we get = 9 ⇒ = 9 ⇒ r = 3 Substituting the value of r in (i) and (ii), we get 3cosθ = –3, 3 sinθ = 0 ⇒ cosθ = – 1, sinθ = 0 ⇒ cosθ = – cos0, sinθ = sin0 Here, cosθ < 0 and sinθ = 0 ∴ θ lies in the second quadrant. ∴ θ = (π – 0) = π. ∴ The required polar form is z = 3(cosπ + i sinπ).
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