Q. 165.0( 3 Votes )

# Find the modulus of each of the following complex numbers and hence express each of them in polar form:

Answer :

= -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 = r^{2}

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 third quadrant.

Tanθ = 1, therefore

Representing the complex no. in its polar form will be

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If z_{1}, z_{2} and z_{3}, z_{4} are two pairs of conjugate complex numbers, prove that

Express in polar form.

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