# Questions on Complex Numbers

## Questions with Answers

### Question 1

Add and express in the form of a complex number \( a + b i \) the expression
\[ \dfrac{(2 + 3i) + (-4 + 5i) - (9 - 3i)}{3} \]
### Question 2

Multiply and express in the form of a complex number \( a + b i \) the expression
\[ (-5 + 3i)(- 4 + 8i) \]
### Question 3

Divide and express in the form of a complex number \( a + b i \) the expression
\[ \dfrac{(-1 - 2i)}{(- 4 + 3i)} \]
### Question 4

Find the complex conjugate to.
\[ 1 + 8 i \]
### Question 5

Express in the form of a complex number \( a + b i \).
\[ \dfrac{(-5 - i)(- 7 + 8i)}{(2 - 4i)} \]
### Question 6

Express in the form of a complex number \( a + b i \).

\[ - (7 - i)(- 4 - 2i)(2 - i) \]
### Question 7

Express in the form of a complex number \( a + b i \).
\[ \dfrac{i}{(1 - i)} \]
### Question 8

Solve for real \( x \) and \( y \) the equation
\[ 2 y + i x = 4 + x - i \]
### Question 9

Find \( a \) and \( b \), where a and b are real numbers so that

\[ a + i b = (2 - i)^2 \]
### Question 10

Find the complex conjugate to
\[ - 3 i \]

## Solution to Above Questions

**question 1:** \( \quad -5 + 9 i\)

**question 2:** \( \quad -4 - 52 i\)

**question 3:** \( \quad - 2 / 25 + (11 / 25) i\)

**question 4:** \( \quad 1 - 8 i\)

**question 5:** \( \quad 109 / 10 + (53 / 10) i\)

**question 6:** \( \quad 70 - 10 i\)

**question 7:** \( \quad -1 / 2 + i / 2\)

**question 8:** \( \quad x = -1 , y = 3 / 2\)

**question 9:** \( \quad a = 3 , b = -4\)

**question 10:** \( \quad 3 i\)
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