If ( z + 1/z ) = 4, then what will be the value of 1/2 ( z² + 1/(z²) ) ?

If ( z + 1/z ) = 4, then what will be the value of 1/2 (…

If ( z + $\frac{1}{z}$ ) = 4, then what will be the value of $\frac{1}{2}$ ( z² + $\frac{1}{z^2}$ ) ?

Show answer & explanation

Correct answer: C

Explanation

The correct answer is option 3 i.e. 7.

Given that

If ( z + $\frac{1}{z}$ ) = 4

Squaring both sides

⇒ z² + $\frac{1}{z^2}$ + 2 = 16

⇒ z² + $\frac{1}{z^2}$ = 14

Hence, ½ ( z² + $\frac{1}{z^2}$ ) = 14/2 = 7