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**Fratricide** Let v = 2 + i and P(z) = z^{3 }- 7z^{2} + 17z - 15

a) Show by substitution that P(2 + i) = 0

b) Find the other two roots of the equation P(z) = 0

c) Let **i** be a unit vector in the positive Re(z) direction and let **j** be a unit vector in the positive Im(z) direction.

Let A be the point on the Argand diagram corresponding to v = 2 + i.

Let B be the point on the Argand diagram corresponding to 1 - 2i.

Show that OA is perpendicular to OB.

d) Find a polynomial with real coefficients and with roots 3, 1 - 2i and 2 + i.

Parts a, b and c were no trouble, but I've never done anything similar (that I know of) to part d before. Could you please point me in the right direction?