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**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

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