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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