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# Chapter 5 Complex Numbers and Quadratic Equations Ex-5.2 Interview Questions Answers

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Question 1 : 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.

Question 2 : 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.

Question 3 : 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.

Question 4 : 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.

Question 5 : 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.

Question 6 : 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.

Question 7 : Convert the given complex number in polar form: Answer 7 : Let r cos θ = and r sin θ = 1
On squaring and adding, we obtain  This is the required polar form.

Question 8 : 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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