Complex numbers – H2 Maths Tuition

Argument of Real and Purely Imaginary Numbers

4a argument of real and imaginary

synthetic division in complex numbers

Supposed we are asked to express f(z) as the product of three quadratic factors with real coefficients, where

The roots worked out to be

Since the roots occur in conjugate pairs, we can use this property:

Therefore,

GC can be very helpful in solving certain problems in Complex Numbers.

Example 1

Use the GC to find the real value of k such that has a complex root 1-i.

Solution

Since 1-i is a root,

Using TI 84 Plus (OS 2.55) to evaluate the complex numbers, we have

2+k = 0

k=-2

Example 2

Find the 2 roots of

Solution

Since the equation is quadratic, we can use the quadratic formula.

Using the GC to evaulate the above,

z = 1+2i or -7i

Many students, including JC H2 math students, have difficulty doing long division when it comes to complex problems.

Try this problem to test or sharpen your long division skills.

Question

If is a factor of , prove by long division that

Solution