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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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