if z= 4 +i7^1/2, then find z^3-4z-9z+91 - Maths - Complex Numbers and Quadratic Equations

Question

if z= 4 +i7^1/2, then find z^3-4z-9z+91?

Munisj Prajapati · Answer

= Z=4+i7^1/2 = Z-4=i7^1/2 = Squaring both side, we get =
(Z-4)^2=i^2 * 7 = Z^2+16-8Z= -7 (i^2=-1) = Z^2+16-8z+7=0 =
Z^2-8z+23=0 (eq 1) = Z^3-4z^2-9z+91 (Given) =
Z(z^2-8z+23)+4(z^2-8z+23)-1 = Z(0) +4(0)-1 = -1 Answer