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If z=4+isqrt(7) , then find the value of...

If `z=4+isqrt(7)` , then find the value of `z^3-4z^2-9z+91.`

A

`23`

B

`i`

C

`-1`

D

`0`

Text Solution

Verified by Experts

The correct Answer is:
C
`z = 4 + I sqrt(7)`
or ` x z- 4 = isqrt(7)`
or ` z^(2) - 8z + 16 = - 7`
or ` z^(2) - 8z + 23 = 0`
Now dividing `z^(3) - 4z^(2) - 9z + 91 ` by `z^(2) - 8z + 23` we get
`z^(3) - 4z^(2) - 9 z + 91 = (z^(2) - 8z + 23) (z +4) - = -1`.
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