Question

The fixed points for the transformation w = (2z-5)/z+4​

Answer 1

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Step-by-step explanation:

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Answer 2

Answer:

The correct answer for this question is −1 ± 2i.

Step-by-step explanation:

We have fixed points are given by:

w = f(z)

z ⇒ $\frac{2z - 5}{z + 4}$ = z

⇒ $z^{2}$ + 2x + 5 = 0

∴ z = −2 ± $\sqrt{4 - 20}$/2

= −2 ± $\sqrt{-16}$/2

= −2 ± 4i/2

= −1 ± 2i

The fixed points or invariant points are the points that coincide with their transformations. The equation z = f yields the fixed points of the transformation w = f(z)(z). In other words, just set w= z and then solve for z to find the fixed point.

Thus, a fixed point of a function in mathematics is an element that the function maps to itself.