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If (x+i y)^3=u+i v ,then show that u/x+...

If `(x+i y)^3=u+i v ,`then show that `u/x+v/y=4(x^2-y^2)`.

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To solve the problem, we need to show that if \((x + i y)^3 = u + i v\), then \(\frac{u}{x} + \frac{v}{y} = 4(x^2 - y^2)\). ### Step-by-Step Solution: 1. **Expand \((x + i y)^3\)**: Using the binomial theorem or the formula for the cube of a binomial, we have: \[ (x + i y)^3 = x^3 + 3x^2(i y) + 3x(i y)^2 + (i y)^3 ...
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