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If ((1+i)/(1-i))^3-((1-i)/(1+i))^3=x+i y...

If `((1+i)/(1-i))^3-((1-i)/(1+i))^3=x+i y ,\ find\ (x , y)`

Text Solution

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Given:`((1+i)/(1-i))^3-((1-i)/(1+i))^3=x+i y`
we have to find x and y
So,
`x+iy=((1+i)/(1-i))^3-((1-i)/(1+i))^3`
`x+iy=((1+i^3+3i(1+i))/(1-i^3-3i(1-i)))-((1-i^3-3i(1-i))/(1+i^3+3i(1+i)))`
since `i^2=-1`
`x+iy=((1-i+3i-3)/(1+i-3i-3))-((1+i-3i-3)/(1-i+3i-3))`
`x+iy=((2i-2)/(-2i-2))-((-2i-2)/(2i-2))`
...
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Knowledge Check

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    A
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    A)( 0,-2)
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    B)(-2,0)
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    C)(0,2)
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  • If ((1 + i)/( 1 - i)) ^(3) - ((1 - i)/( 1 + i)) ^(3) = x + iy then (x, y) is

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