If -a-ib-x-iy- then possible value of -a-ib is

The correct option is D x iy √(a+ib)=x+iy ⇒ a+ib=(x+iy)^2=x^2 y^2+2ixy ⇒ a=x^2 y^2 ,b=2xy a ib=x^2 y^2 2ixy =x^2+(iy)^2 2ixy ...

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Equality of 2 Complex Numbers

If √a+ib=x+...

Question

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

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x - i y

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Solution

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Similar questions

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

\sqrt{a - i b}

x^{2} + y^{2}

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

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

x + i y = \frac{a + i b}{a - i b}

x^{2} + y^{2} = 1

a + i b = \frac{x + i y}{x - i y}

a^{2} + b^{2} = 1

\frac{b}{a} = \frac{2 x y}{x^{2} - y^{2}}

\frac{(a + i b)}{(c + i d)} = x + i y

\frac{a - i b}{c - i d} = x - i y

\frac{a^{2} + b^{2}}{c^{2} + d^{2}} = x^{2} + y^{2}

x + i y = \sqrt{\frac{a + i b}{c + i d}}

x^{2} + y^{2}

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