Question

$\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \sf{( - 1)^{ π} =x} \: \: \: \: \: \: \sf \: {find \: the \: value \: of \: x } \\ \\ \\ \\ \\ \\ \ \textless \ br /\ \textgreater \ HNY21$
​

Answer 1

We start with the formula:

eiθ = cos θ + i sin θ

Substituting θ = π gives the famous formula:

eiπ = cos π + i sin π = -1

Now we raise both sides to the power of π to get:

(-1)π

= (eiπ)π

= eiπ2

Now we let θ = π2 to get:

eiπ2

= cos π2 + i sin π2

≈ -0.903 – (0.430)i