Q10 of 11 Page 5

Find the modulus and the arguments of each of the complex numbers
(i) 1 – i   (ii) –1 + i


(i) 1 – i   
x= rcosθ=1;y = rsinθ=−1
x + iy = 1 – i

x = 1, y = -1
r =

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

(ii) –1 + i
x= rcosθ=−1;y = rsinθ=1
x + iy = -1 + i

x = -1, y = 1

r =

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

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i. = 0        ii. x + 3 = 0            
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Find the modulus and the arguments of each of the complex numbers 
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Find the modulus and the arguments of each of the complex numbers
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