Question

 

If (x+1)/(1+i)+(y-1)/(1-i)=i then value of x + y =​

Answer 1

Answer:

$x + y = i(3 - {i}^{2} + x - y)$

Step-by-step explanation:

$\frac{x + 1}{1 + i} + \frac{y - 1}{1 - i} = i$

$\frac{(x + 1)(1 - i) + (y - 1)(1 + i)}{(1 + i)(1 - i)} = i$

$\frac{(x - ix + 1 - i) + (y + iy - 1 - i)}{1 - i + i - {i}^{2} } = i$

$\frac{x - ix - i + y + iy - i}{1 - {i}^{2} } = i$

$x + y - ix + iy - 2i = (1 - {i}^{2} )i$

$x + y - ix + iy = i - {i}^{3} + 2i$

$x + y - ix + iy = 3i + {i}^{3}$

$x + y = 3i - {i}^{3} + ix - iy$

$x + y = i(3 - {i}^{2} + x - y)$

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