Chapter 5 Complex Numbers and Quadratic Equations Ex 5.2 Solutions
Question - 1 : - Find the modulus and the argument of the complex number 
Answer - 1 : -
On squaring and adding, we obtain
Since both the values of sin θ and cos θ are negative and sinθ and cosθ are negative in III quadrant,
Thus, the modulus and argument of the complex number 
are 2 and 
respectively.
Answer - 2 : -
On squaring and adding, we obtain
Thus, the modulus and argument of the complex number
are 2 and 
respectively.Answer - 3 : -
1 – i
Let r cos θ = 1 and r sin θ = –1
On squaring and adding, we obtain
This is the required polar form.
Question - 4 : - Convert the given complex number in polar form: – 1 + i
Answer - 4 : -
– 1 + i
Let r cos θ = –1 and r sin θ = 1
On squaring and adding, we obtain
It can be written,
This is the required polar form.
Question - 5 : - Convert the given complex number in polar form: – 1 – i
Answer - 5 : -
– 1 – i
Let r cos θ = –1 and r sin θ = –1
On squaring and adding, we obtain
This is the required polar form.
Question - 6 : - Convert the given complex number in polar form: –3
Answer - 6 : -
–3
Let r cos θ = –3 and r sin θ = 0
On squaring and adding, we obtain
This is the required polar form.
Question - 7 : - Convert the given complex number in polar form: 
Answer - 7 : -
Let r cos θ =
and r sin θ = 1On squaring and adding, we obtain
This is the required polar form.
Question - 8 : - Convert the given complex number in polar form: i
Answer - 8 : -
i
Let r cosθ = 0 and r sin θ = 1
On squaring and adding, we obtain
This is the required polar form.