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Find the modulus and the argument of the complex number
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.
Find the modulus and the argument of the complex number
On squaring and adding, we obtain
Thus, the modulus and argument of the complex number 
are 2 and
respectively.
Convert the given complex number in polar form: 1 – i
1 – i
Let r cos θ = 1 and r sin θ = –1
On squaring and adding, we obtain
This is the required polar form.
Convert the given complex number in polar form: – 1 + i
– 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.
Convert the given complex number in polar form: – 1 – i
– 1 – i
Let r cos θ = –1 and r sin θ = –1
On squaring and adding, we obtain
This is the required polar form.
Convert the given complex number in polar form: –3
–3
Let r cos θ = –3 and r sin θ = 0
On squaring and adding, we obtain
This is the required polar form.
Convert the given complex number in polar form: 
Let r cos θ =
and r sin θ = 1
On squaring and adding, we obtain
This is the required polar form.
Convert the given complex number in polar form: i
i
Let r cosθ = 0 and r sin θ = 1
On squaring and adding, we obtain
This is the required polar form.
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