Learning Resources

Focus B: Complex Numbers and their Graphs

Things to remember about the Argand diagram:

• Points on the real axis are all real numbers; that is, in the form a + oi.
• Points on the imaginary axis are all imaginary numbers; that is, in the form 0 + bi.
• All other points are in the complex form a + bi, where neither a nor b are equal to zero.

An equation a + bi = c + di will be true if and only if the real parts are equal and the imaginary parts are equal. In other words, if and only if a = c and b = d.

The absolute value, or modulus, of a complex number a + bi can be found using the formula . This represents the length of the position vector.