# NCERT Class 11-Math's: Chapter –5 Complex Numbers and Quadratic Equations Part 8

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**Question 32:**

Number of solutions of the equation is

(A) 1

(B) 2

(C) 3

(D) Infinitely many

**Answer: (D)**

Therefore,

So can have any real value. Hence infinitely many solutions.

**Question 33:**

The amplitude of is

(A)

(B)

(C)

(D)

**Answer: (D)**

Here and

Therefore,

**5.3 EXERCISE**

## Short Answer Type

**Question 1:**

For a positive integer *,* find the value of

**Answer:**

**Question 2:**

**Answer:**

**Question 3:**

If then find.

**Answer:**

**Question 4:**

If , then find the value of .

**Answer:**

**Question 5:**

If then find .

**Answer:**

**Question 6:**

If , find the value of .

**Answer:**

**Question 7:**

If , then show that .

**Answer:**

Given

Rationalizing the denominator,

Hence proved.