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:
GC can be very helpful in solving certain problems in Complex Numbers.
Use the GC to find the real value of k such that has a complex root 1-i.
Since 1-i is a root,
Using TI 84 Plus (OS 2.55) to evaluate the complex numbers, we have
2+k = 0
Find the 2 roots of
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.
If is a factor of , prove by long division that