Question 1403a

Complex Numbers
Conjugate Root Theorem

Question

It is given that z1=43i{z_1 = 4 - 3 \mathrm{i}} is a root of the equation
z310z2+41z50=0.z^3 - 10 z^2 + 41 z - 50=0.
The equation has two other roots, z2{z_2} and z3,{z_3,} where z2{z_2} is complex and z3{z_3} is real. Find z3.{z_3.}

Attempt

z3={z_3 = }

Answer

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