Question

How can i solve this KIND OF VALUE (〖-i)〗^i

Answer 1

we might write -i as cos 3pi/2 + i sin 3pi/2 = e^(i 3pi/2)


so -i^i = [e^(i 3pi/2)]^i = e^ -3pi/2 = approx 0.00898

Answer 2

a rational number Surprising result.

Answer 3

is that imaginary number?

Answer 4

well i is but 00898 isn't

Answer 5

oh ok, i thought it was just an imaginary number to the power of i is,,that will be equal to 1.

Answer 6

I should have said 0.00898 is a real number - it might not be rational.

Answer 7

there are some remarkable results sometimes when you play with complex numbers.
the Euler equation is derived from comples numbers also

e^i pi = cos pi + i sin pi = -1 + 0i = -1

so e ^ i pi + 1 = 0
This equation unites the 5 most important numbers in mathematics: 0 , 1, pi, e, and i.

Answer 8

Thanks DEAR