Location of Complex Roots of a Real Quadratic

k

surface

none

real part

complex part

both

function:

2

z

-4z

zeros: {0,4}

This Demonstration shows the location of the real or complex roots of the real-valued function

f(x)=

2

x

-4x+k

. The real-valued parabola (yellow contour) is superimposed on the plot of the surface of the real component

Re(f(z))

. The zeros of

f(z)

are then those values for which the real and imaginary components are zero simultaneously. The real surface is plotted and the level curve where the real part is zero (purple) is shown. Similarly, the imaginary surface is plotted and the level curve where the imaginary part is zero (green) is shown. Where the purple and green lines meet are the values where the function is zero, and these spots are illustrated by red dots.