Question 708501: what are all of the zeros of the equation: 4i and 2-3i?
Answer by josgarithmetic(39631)   (Show Source):
You can put this solution on YOUR website! The question about the listed information does not make sense. What you might be trying to ask is, what is an equation for which the zeros are 4i and 2-3i.
The change being as I describe, you will need to include two more numbers: 2+3i and -4i. You will have an equation possibly like (x-a)(x-b)(x-c)(x-d)=0. You will use each of the given zeros to separately determine a, b, c, and d.
I will do ONE of these as an example to help you start.
Using the zero, 4i, we may have that (x-a)=0, and we expect ((4i)-a)=0.
4i-a=0
4i=-a
-a=4i
a=-4i.
So this test shows that one of the binomial factors is (x-a)=(x-(-4i))=(x+4i).
Naturally we must also test the zero -4i, and we should find that another binomial factor must be... (x-4i).
So far, we have (x+4i)(x-4i)(x-c)(x-d)=0;
I leave the other two factors undone and for you to try to finish.
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