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# Polar form of a complex number solutions

Polar form of a complex number. If z= x + iy is a complex number. Then z = r ( cosθ + sinθ ) is called polar form or trigonometric form of a complex number.

By comparing real and imaginary parts of a complex number,  we get
x = r cosθ           (1)
y = r sinθ           (2)

By squaring above equations and adding we get

EXAMPLE

Express in polar form.

Solution

With and y = −1 we obtain

Now

and

which is an angle whose terminal side is in the first quadrant.But

since the point lies in the third quadrant, we take the solution
So,
Therefore, polar form of the number is

Solved Questions of polar form
CHALLENGE

write the given complex number in polar form first using an argument θ = Arg(z)
1.       2
2.    −10
3.     −3i
4.       6i
5.       1 + i
6.       5 − 5i
8.
9.
10.

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### One comment

1. Plz provide the solution