Question

If [(1 + i)/(1 - i)]³ – [(1 - i)/(1 + i)]³ = x + iy, find (x, y)

Answer 1

Given as

[(1 + i)/(1 - i)]³ – [(1 - i)/(1 + i)]³ = x + iy

Now let us rationalize the denominator, we get

i³–(-i)³ = x + iy

2i³ = x + iy

2i².i = x + iy

2(-1)I = x + iy

-2i = x + iy

By equating real and imaginary parts on both sides we get

x = 0 and y = -2

Thus, the values of x and y are 0 and -2.