Question

Find a polynomial with integer coefficients, with leading coefficient 1, degree 5, zeros i and 3- i, and passing through the origin.

Answer 1

The answer is

Answer 2

If it passes through the origin there is another solution at x = 0.
If i is a zero then -i is another zero since complex roots come in conjugate pairs that way.
Likewise, if 1-i is a zero then 1 + i is also a zero.
Use the factor theorem to convert these five zeros into factors:
(x + 0) (x + i) (x - i) (x - 1 + i) (x - 1 - i)
Multiply these factors together:
x^5 - 2x^4 + 3x^3 - 2x^2 + 2x

Answer 3

Excellent work, Nerd! But next time, let the other person do some of the work, with your guidance. He or she could have multiplied those factors together.