Question

If root over x+iy = a+ib , then prove that root over x-iy = a-ib ... ​

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

If  $\sqrt{x+iy}=a+ib$  then $\sqrt{x-iy}=a-ib$.

Step-by-step explanation:

It is given that

$\sqrt{x+iy}=a+ib$

Taking square on both sides.

$x+iy=(a+ib)^2$

$x+iy=a^2+(ib)^2+2abi$

$x+iy=a^2-b^2+2abi$             $[\because i^2=-1]$

On comparing both sides we get

$x=a^2-b^2,y=2ab$

$x-iy=(a^2-b^2)-2abi$

$x-iy=a^2+(ib)^2-2abi$

$x-iy=(a-ib)^2$

Taking square root on both sides.

$\sqrt{x-iy}=a-ib$

Hence proved.

#Learn more

X+iy=a+ib/a-ib,prove that x^2​.

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