If \(\sqrt{a+ib}\) = x+iy, then possible value of\(\sqrt{a-ib}\) is�

1.	If \(\sqrt{a+ib}\) = x+iy, then possible value of\(\sqrt{a-ib}\) is A. x2 + y2B. \(\sqrt{x^2 + y^2}\)C. x + iy D. x – iy E. \(\sqrt{x^2 - y^2}\)
Answer» \(\sqrt{a+ib}\) = x+iy Square both sides a + ib = (x + iy)² = x² + i2xy - y² So, we can say that a = x² – y² and b = 2xy a – ib = (x²– y²) – i(2xy) = (x)² + 2(x)(-iy) + (-iy)² = (x + (-iy))² = (x – iy)² \(\sqrt{a-ib}\) = x-iy

If \(\sqrt{a+ib}\) = x+iy, then possible value of\(\sqrt{a-ib}\) is A. x2 + y2B. \(\sqrt{x^2 + y^2}\)C. x + iy D. x – iy E. \(\sqrt{x^2 - y^2}\)

Answer»

\(\sqrt{a+ib}\) = x+iy

Square both sides

a + ib = (x + iy)² = x² + i2xy - y²

So, we can say that a = x² – y² and b = 2xy

a – ib = (x²– y²) – i(2xy)

= (x)² + 2(x)(-iy) + (-iy)²

= (x + (-iy))²

= (x – iy)²

\(\sqrt{a-ib}\) = x-iy