Question

70 points answer plzz

Answer 1

Z - 1/Z = 6

On squaring both sides, we get

Z^2 + 1 /Z^2 - 2(Z)( 1/ Z) = 36

=> Z^2 + 1/Z^2 - 2 = 36

=> Z^2 + 1/Z^2 = 38 ---------(1)

Now,

( Z + 1/ Z) ^2 = Z^2 + 1/Z^2 + 2(Z) (1/Z)

( Z + 1/ Z) ^2= Z^2 + 1/Z^2 + 2

( Z + 1/ Z) ^2= 38 + 2

( Z + 1/ Z) ^2= 40

$z + \frac{1}{z} = \sqrt{40} \\ \\ = 2 \sqrt{10}$

Now,

On squaring both sides of equation (1), we get,


Z^4 + 1 / Z^4 + 2(Z^2) (1/Z^4) = 1444

=> Z^4 + 1 / Z^4 + 2 = 1444

=> Z^4 + 1 / Z^4 = 1442

Answer 2

Given z - 1/z = 6.

(i)

We know that (z + 1/z)^2 = (z - 1/z)^2 + 4

                                         = (6)^2 + 4

                                         = 36 + 4

                                         = 40.

 $z + \frac{1}{z} = \sqrt{40}$.


(2)

On squaring both sides, we get

$(z + \frac{1}{z} )^2 = ( \sqrt{40} )^2$

$z^2 + \frac{1}{z^2} + 2 * z * \frac{1}{z} = 40$

$z^2 + \frac{1}{z^2} + 2 = 40$

$z^2 + \frac{1}{z^2} = 40 - 2$

$z^2 + \frac{1}{z^2} = 38$



(3)

On squaring both sides, we get

$(z^2 + \frac{1}{z^2} )^2 = (38)^2$

$z^4 + \frac{1}{z^4} + 2 * z^2 * \frac{1}{z^2} = 1444$

$z^4 + \frac{1}{z^4} + 2 = 1444$

$z^4 + \frac{1}{z^4} = 1444 - 2$

$z^4 + \frac{1}{z^4} = 1442$



Hope this helps!