$\sqrt{-x}$

asked by guest
on Nov 16, 2024 at 5:53 am



You asked:

Evaluate the expression: \(\sqrt{-x}\)

MathBot Answer:

\[\sqrt{-x} = \sqrt{- x}\]

Roots

\[\sqrt{-x} = i \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(x\right)},- \operatorname{re}{\left(x\right)} \right)}}{2} \right)} + \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(x\right)},- \operatorname{re}{\left(x\right)} \right)}}{2} \right)} \approx i \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{0.25} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(x\right)},- \operatorname{re}{\left(x\right)} \right)}}{2} \right)} + \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{0.25} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(x\right)},- \operatorname{re}{\left(x\right)} \right)}}{2} \right)}\]\[\sqrt{-x} = i \left(- \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(x\right)},- \operatorname{re}{\left(x\right)} \right)}}{2} \right)}\right) - \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(x\right)},- \operatorname{re}{\left(x\right)} \right)}}{2} \right)} \approx - i \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{0.25} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(x\right)},- \operatorname{re}{\left(x\right)} \right)}}{2} \right)} - \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{0.25} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(x\right)},- \operatorname{re}{\left(x\right)} \right)}}{2} \right)}\]

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