Q. 115.0( 1 Vote )

# Find the modulus and the arguments of each of the complex numbers (i) –3     (ii) (iii) i

(i) –3
x + iy = -3
x = -3, y = 0
r = and tan θ = y/x = 0/3, θ = π .
Thus, the polar coordinates of –1+ i are (3, π ) and its polar form is 3(cos π + i sinπ ).

(ii) x + iy = + i
x = , y = 1
r = and tan θ = y/x = , θ = π /6.
Thus, the polar coordinates of + i are (2, π /6) and its polar form is 2(cos + i sin ).

(iii) i
x + iy = i
x = 0, y = 1
r = and tan θ = y/x = ∞ , θ = .
Thus, the polar coordinates of –1+ i are (1, ) and its polar form is (cos + i sin ).

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