Question

Express the following complex numbers in polar form and hence
find the modulus and argument in each case:
i)root 3+i
ii) -2+ 2i
(iv)-root 3+i
v) 1-i/1+i
(vii) -2 -3i
(viii)- 3

Answer 1

Answer:

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Answer 2

Answer:

As we know that the polar form of a complex number Z = x + iy is given by Z = |Z|(cos θ + i sin θ) Where, |Z| = modulus of complex number = √(x2 + y2) θ = arg (z) = argument of complex number = tan-1(|y|/|x|)Read more on Sarthaks.com - https://www.sarthaks.com/660533/find-the-modulus-argument-the-following-complex-numbers-hence-express-each-them-polar-form

i)√3+i

Given as Z = √3 + i Therefore now, |Z| = √(x2 + y2) = √((√3)2 + 12) = √(3 + 1) = √4 = 2 θ = tan-1(|y|/|x|) = tan-1(1/√3) Here x > 0, y > 0 complex number lies in 1st quadrant and the value of θ is 0° ≤ θ ≤ 90°. θ = π/6 Z = 2(cos (π/6) + i sin (π/6)) ∴ Polar form

of (√3 + i) is 2(cos (π/6) + i sin (π/6))Read more on Sarthaks.com - https://www.sarthaks.com/660533/find-the-modulus-argument-the-following-complex-numbers-hence-express-each-them-polar-form