Question

If z = 4 + i $\sqrt{7}$ , then value of $z^3-4z^2-9z+91$ equals

• A. 0
• B. 1
• C. -1
• D. 2

Answer 1

The correct option is C

-1

\(z = 4 + i \sqrt{7}\\

{\Rightarrow}z^2 - 8z + 23 = 0 - (1) \\

z^3 - 8z^2 + 23z = 0 - (2) \\

z^3 - 4z^2 - 92 + 91 \\

= ( z^3 - 8z^2 + 23z ) + ( 4z^2 + 32z+92) - 1 = -1 \\

[using (1) and (2) ] \)