Questions on Complex Numbers

Questions with answers on complex numbers. In what follows i denotes the imaginary unit defined by i = √ ( -1 ).

Questions with Answers

Question 1

Add and express in the form of a complex number a + b i.
(2 + 3i) + (-4 + 5i) - (9 - 3i) / 3

Question 2

Multiply and express in the form of a complex number a + b i.
(-5 + 3i)(- 4 + 8i)

Question 3

Divide and express in the form of a complex number a + b i.
(-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.
(-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.
i / (1 - i)

Question 8

Solve for x and y where x and y are real numbers.
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: -5 + 9 i
question 2: -4 - 52 i
question 3: -2 / 25 + (11 / 25) i
question 4: 1 - 8 i
question 5: 109 / 10 + (53 / 10) i
question 6: 70 - 10 i
question 7: -1 / 2 + i / 2
question 8: x = -1 , y = 3 / 2
question 9: a = 3 , b = -4
question 10: 3 i

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