If x+iy = (1+i)^6 - (1-i)^6,then which one of | vedclass

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(B) We have,$x+iy = (1+i)^6 - (1-i)^6$. First,calculate $(1+i)^2 = 1 + i^2 + 2i = 1 - 1 + 2i = 2i$. Then,$(1+i)^6 = ((1+i)^2)^3 = (2i)^3 = 8i^3 = -8i$

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$x+y=-16$

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(B) We have,$x+iy = (1+i)^6 - (1-i)^6$. First,calculate $(1+i)^2 = 1 + i^2 + 2i = 1 - 1 + 2i = 2i$. Then,$(1+i)^6 = ((1+i)^2)^3 = (2i)^3 = 8i^3 = -8i$. Similarly,$(1-i)^2 = 1 + i^2 - 2i = 1 - 1 - 2i = -2i$. Then,$(1-i)^6 = ((1-i)^2)^3 = (-2i)^3 = -8i^3 = 8i$. Substituting these values back into the equation: $x+iy = (-8i) - (8i) = -16i$. Comparing the real and imaginary parts,we get $x = 0$ and $y = -16$. Therefore,$x+y = 0 + (-16) = -16$.

If $x+iy = (1+i)^6 - (1-i)^6$,then which one of the following is true?

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