Question

(1-i)^3/(1+i)^3 is equal to ??​

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Secondary SchoolMath 8 points

If (1+i/1-i)3 - (1-i/1+i)3 = x+iy, then find (x,y)

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ARoy

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(1+i/1-i)³-(1-i/1+i)³=x+iy

or, x+iy=[(1³+3i+3i²+i³)/(1³-3i+3i²-i³)]-[(1³-3i+3i²-i³)/(1³+3i+3i²+i³)]

or, x+iy={1+3i+3(-1)+(-1).i}/{1-3i+3(-1)-(-1).i}-{1-3i+3(-1)-(-1).i}/{1+3i+3(-1)+(-1).i}

or, x+iy=(1+3i-3-i)/(1-3i-3+i)-(1-3i-3+i)/(1+3i-3-i)

or, x+iy=(-2+2i)/(-2-2i)-(-2-2i)/(-2+2i)

or, x+iy={(-2)(1-i)/(-2)(1+i)}-{(-2)(1+i)/(-2)(1-i)}

or, x+iy=[(1-i/1+i)-(1+i/1-i)

or, x+iy={(1-i)²-(1+i)²}/{(1)²-(i)²}

or, x+iy=(1-2i+i²-1-2i-i²)/{1-(-1)}

or, x+iy=(-4i)/(1+1)

or, x+iy=-4i/2

or, x+iy=-2i

or, x+iy=0+i.(-2)

where x=0 and y=-2