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

The correct option is D √(a+ib) = x+iy ⇒ (√((a+ib)))^2 =(x+iy)^2 ⇒ a=x^2 y^2, b=2xy And hence √(a ib) =√(x^2 y^3 2xyi)=√((x+yi)^2) = x iy Note: In the questio ...

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Standard XII

Mathematics

Equality of 2 Complex Numbers

If √a+i b=x+i...

Question

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

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Solution

The correct option is D

$\sqrt{a + i b}$ = x+iy $\Rightarrow$ ${(\sqrt{(a + i b)})}^{2}$ = $(x + i y)^{2}$

$\Rightarrow$ a= $x^{2}$ - $y^{2}$ , b=2xy And hence

$\sqrt{a - i b}$ = $\sqrt{x^{2} - y^{3} - 2 x y i}$ = $\sqrt{(x + y i)^{2}}$ = x-iy

Note: In the question, it should have been given that a,b,x,y belongs to R.

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

The correct option is D √a+ib = x+iy ⇒ (√(a+ib))2 =(x+iy)2 ⇒ a=x2-y2, b=2xy And hence √a−ib =√x2−y3−2xyi=√(x+yi)2 = x-iy Note: In the question, it should have been given that a,b,x,y belongs to R.

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