Find the modulus

= i + 1

Let Z = 1 + i = r(cosθ + isinθ)

Now , separating real and complex part , we get

1 = rcosθ ……….eq.1

1 = rsinθ …………eq.2

Squaring and adding eq.1 and eq.2, we get

2 = r²

Since r is always a positive no., therefore,

r = √2,

hence its modulus is √2.

now , dividing eq.2 by eq.1 , we get,

Tanθ = 1

Since , and tanθ = 1. therefore the θ lies in first quadrant.

Tanθ = 1, therefore

Representing the complex no. in its polar form will be

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