Complex Numbers and Quadratic Equations Exercise 5.2

Exercise 5.2

Find the modulus and the argument of each of the complex numbers in exercises 1 to 2.

1.

Ans. Given:

and

Squaring both sides and adding both the equations, we get

and

and

[ lies in third quadrant]

Therefore, and arg

2.

Ans. Given:

and

Squaring both sides and adding both the equations, we get

and

and

[ lies in second quadrant]

Therefore, and arg

Convert each of the complex numbers given in Exercises 3 to 8 in the polar form.

3.

Ans. Given:

and

Squaring both sides and adding both the equations, we get

and

and

[ lies in fourth quadrant]

Therefore, Polar form of is

4.

Ans. Given:

and

Squaring both sides and adding both the equations, we get

and

and

[ lies in second quadrant]

Therefore, Polar form of is

5.

Ans. Given:

and

Squaring both sides and adding both the equations, we get

and

and

[ lies in third quadrant]

Therefore, Polar form of is

6.

Ans. Given:

and

Squaring both sides and adding both the equations, we get

and

and

[ lies in second quadrant]

Therefore, Polar form of is

7.

Ans. Given:

and

Squaring both sides and adding both the equations, we get

and

and

[ lies in first quadrant]

Therefore, Polar form of is

8.

Ans. Given:

and

Squaring both sides and adding both the equations, we get

and

and

[ lies in first quadrant]

Therefore, Polar form of is