Questions: Arithmetic on complex numbers
Before attempting these questions, it is highly recommended that you read Guide: Arithmetic on complex numbers.
Q1
Work out each of the following expressions, expressing your answer in the form \(a+bi\) where \(a\) is the real part and \(b\) is the imaginary part.
1.1. \(\quad (5+7i)-(2+3i)\)
1.2. \(\quad (8+6i)+(2-4i)\)
1.3. \(\quad (4-i\sqrt{2})-(3+i\sqrt{7})\)
1.4. \(\quad (\sqrt{8}+4i)-(\sqrt{5}+2i)\)
1.5. \(\quad (\sqrt{7}+3i)+(2-i)\)
1.6. \(\quad (5 + i\sqrt{2}) - (7 - i) + (\sqrt{3} + 4i)\)
Q2
Work out each of the following expressions, expressing your answer in the form \(a+bi\) where \(a\) is the real part and \(b\) is the imaginary part.
2.1. \(\quad (2+3i)(4+5i)\)
2.2. \(\quad (3+i)(2-i)\)
2.3. \(\quad 4(6+3i)\)
2.4. \(\quad (1+i)^2\)
2.5. \(\quad (3+2i)^3\)
2.6. \(\quad (7-4i)^2(i-2)\)
2.7. \(\quad (1 - i\sqrt{3})^3\)
2.8. \(\quad (5-2i)(5+2i)\)
2.9. \(\quad (\sqrt{2} + i\sqrt{3})(\sqrt{8} - i\sqrt{3})\)
Q3
Work out each of the following expressions, expressing your answer in the form \(a+bi\) where \(a\) is the real part and \(b\) is the imaginary part.
3.1. \(\quad \dfrac{7-6i}{1+2i}\)
3.2. \(\quad \dfrac{4-i}{1+4i}\)
3.3. \(\quad \dfrac{3}{5i}\)
3.4. \(\quad \dfrac{4+2i}{3-i}\)
3.5. \(\quad \dfrac{9+i}{i}\)
3.6. \(\quad \dfrac{-2-2i}{-2+2i}\)
3.7. \(\quad \dfrac{1+5i}{-3i}\)
3.8. \(\quad \dfrac{-4}{1-i}\)
3.9. \(\quad \dfrac{1-3i}{1+2i}\)
Q4
Work out each of the following expressions, expressing your answer in the form \(a+bi\) where \(a\) is the real part and \(b\) is the imaginary part.
4.1. \(\quad \dfrac{(6+4i)(3-i)}{2i}\)
4.2. \(\quad 3i(5-4i)+(6+2i)\)
4.3. \(\quad (2+3i)(1-i)-(5-4i)\)
4.4. \(\quad \dfrac{(5+2i)+(4-i)}{1+i}\)
4.5. \(\quad \dfrac{(2+i)^3}{(3+i)-(1+i)}\)
4.6. \(\quad (\dfrac{6-3i}{2(1-i)})^2\)
After attempting the questions above, please click this link to find the answers.
Version history and licensing
v1.0: initial version created 11/24 by Charlotte McCarthy as part of a University of St Andrews VIP project.