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 