If -a-i b-x-i y- then possible value of -a-i b is

The correct option is B x iy √(a+ib)=x+iy Squaring on both sides, we get, a+ib=x^2+(iy)^2+2ixy ⇒ a+ib=(x^2 y)^2+2ixy ∴ a=(x^2 y^2) and b = 2xy ∴ a ib=(x^2 y^ ...

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Byju's Answer

Standard XII

Mathematics

Equality of 2 Complex Numbers

If √a+i b==x+...

Question

If $\sqrt{a + i b} =$ = x + iy, then possible value of $\sqrt{a - i b}$ is

$x^{2} + y^{2}$

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$\sqrt{x^{2} + y^{2}}$

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x + iy

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x - iy

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$\sqrt{x^{2} - y^{2}}$

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Solution

The correct option is D
x - iy

$\sqrt{a + i b} = x + i y$

Squaring on both sides, we get,

$a + i b = x^{2} + (i y)^{2} + 2 i x y \Rightarrow a + i b = (x^{2} - y)^{2} + 2 i x y ∴ a = (x^{2} - y^{2}) and b = 2xy ∴ a - i b = (x^{2} - y^{2}) - 2 i x y \Rightarrow a - i b = x^{2} + i^{2} y^{2} - 2 i x y [∵ i^{2} = - 1]$

Taking square root on both sides, we get :

$\sqrt{a - i b} = x - i y$

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If √a+ib== x + iy, then possible value of √a−ib is

The correct option is D x - iy √a+ib=x+iy Squaring on both sides, we get, a+ib=x2+(iy)2+2ixy⇒ a+ib=(x2−y)2+2ixy∴ a=(x2−y2)and b = 2xy∴ a−ib=(x2−y2)−2ixy⇒ a−ib=x2+i2y2−2ixy [∵ i2=−1] Taking square root on both sides, we get : √a−ib=x−iy

If $\sqrt{a + i b} =$ = x + iy, then possible value of $\sqrt{a - i b}$ is