Complex numbers

2
3
4 4 − 8 + 6 − 2
=4=z8=6=z2==







= n






= n





A plot of the function is shown below,





















As you can see the function passes through the x-axis

when x = 1, the real root.

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Example 14:

So far we have looked at many complex roots, this

example shows how they can be related to locations

in the argand diagram. The plot of the function
2
= 4 + 3 + 2 is shown below.




















It is quite clear the roots are complex; show the
function reflected about the minimum.






















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Add a circle whose diameter intersects the roots of

the reflected function.

























o
Rotate the circle through 90 ,



























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Find the roots of the original equation,

2
4 + 3 + 2

(MODE)53 4=3=2=


= n







= n










When you zoom in on the

circle you will see the
coordinates of the original

intersects correspond to the

complex root values of the
quadratic equation,




(-0.375, 0.599i) and (-0.375, -0.599i).




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If you wish to further your knowledge of complex

numbers you are recommended to work through
Matrices and Complex Numbers from,


www.CambridgePaperbacks.com















































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