MEI online resources for mathematics
The Further Mathematics Network

Teachers' resources for complex numbers

Introduction to Complex Numbers

Before you start...

• You need to be able to use the quadratic formula to solve quadratic equations.

When you have finished you should...

• Be able to add, subtract, multiply and divide complex numbers.
• Know what is meant by a complex conjugate.
• Be able to find the solutions of any quadratic equation with real coefficients, and know that non-real roots occur in conjugate pairs.

The Argand diagram and the modulus-argument form

Before you start...

• You need to have covered section 1.
• You need to know the trigonometry work from C2, including radians, and the sine, cosine and tangent of angles greater than 90°. If you have not yet covered this work, there are some additional notes to help you.

When you have finished you should...

• Represent complex numbers geometrically by means of an Argand diagram.
• Understand the geometrical effects of conjugating a complex number and of adding and subtracting two complex numbers.
• Understand the meanings of the modulus and argument of a complex number.
• Be able to find the modulus and argument of a complex number.
• Know that |z1z2| = |z1||z2|.

Complex numbers and equations

Before you start...

• You need to have covered sections 1 and 2.
• You need to be able to use the quadratic formula to solve quadratic equations.
• You should be familiar with the factor theorem.
• You need to be able to divide a cubic or quartic expression by a linear or quadratic factor.
• You need to be able to solve a pair of simultaneous equations.

When you have finished you should...

• Know that non-real roots of any polynomial equation with real coefficients occur in conjugate pairs.
• Be able to find the two square roots of a complex number.
• Be able to solve equations involving complex numbers by comparing real and imaginary parts.