Question

if z-1/z =4,then z^2-1/z^2 =
a)14 b)16 c)18 d)8​

Answer 1

Answer

±8√5

Method

The question can be solved with identity.

The revised form will be used here.

First here is 2nd-Degree identity

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

Its revised form is

-  $z^2+\frac{1}{z^2}=(z-\frac{1}{z})^2 +2$  ∴$z^2+\frac{1}{z^2}=18$

Second here is revised identity

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

Now, substitute the value.

$(z^2-\frac{1}{z^2})^2=324-4=320$

And,

$z^2-\frac{1}{z^2}$ will be ±8√5.