# NCERT Class 11-Math՚s: Chapter – 5 Complex Numbers and Quadratic Equations Part 11 (For CBSE, ICSE, IAS, NET, NRA 2023)

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**Question 20**:

If for complex numbers , , then show that

**Answer**:

Let

Given

Now,

We know that

Hence proved.

**Question 21**:

Solve the system of equations .

**Answer**:

Given

Let

Then

Given

Also,

Now,

Solving (1) and (2) , we get

Hence, we have four complex numbers.

**Question 22**:

Find the complex number satisfying the equation

**Answer**:

Given equation

Putting we get

Comparing real and imaginary parts to zero, we get

And

Putting into , we get

**Question 23**:

Write the complex number in polar form.

**Answer**:

Given