Question

Find all x and y between 0 and 2pi so that the equation is ture
-2 cosx -i sin y = 2 sinx +i

i am also having trouble with this one
Simplify the power of i



i to the 39th power

Answer 1

i^1 = i
i^2 = -1
i^3 = -i
i^4 = (i^2)^2 =-1^2 = 1

i^38 =(i^2)^19 = -1
so
i^39 = -1*i = -i

Answer 2

If -2 cosx -i sin y = 2 sinx +i
both the real and imaginary terms on opposite sides of the equation must be equal.
-2 cos x = 2 sin x
Divide both sides by 2 cos x to solve for x
-1 = tan x
x = 3 pi/4 and 7 pi/4

From the imaginary part of the equation
sin y = -1
y = (3/2) pi