# Questions on Complex Numbers

### 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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