$\sqrt{1-x}$

asked by guest
on Nov 19, 2024 at 3:29 pm



You asked:

Evaluate the expression: \(\sqrt{1 - x}\)

MathBot Answer:

\[\sqrt{1 - x} = \sqrt{1 - x}\]

Roots

\[\sqrt{1 - x} = i \sqrt[4]{\left(1 - \operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(x\right)},1 - \operatorname{re}{\left(x\right)} \right)}}{2} \right)} + \sqrt[4]{\left(1 - \operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(x\right)},1 - \operatorname{re}{\left(x\right)} \right)}}{2} \right)} \approx i \left(\left(1.0 - \operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{0.25} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(x\right)},1 - \operatorname{re}{\left(x\right)} \right)}}{2} \right)} + \left(\left(1.0 - \operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{0.25} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(x\right)},1 - \operatorname{re}{\left(x\right)} \right)}}{2} \right)}\]\[\sqrt{1 - x} = i \left(- \sqrt[4]{\left(1 - \operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(x\right)},1 - \operatorname{re}{\left(x\right)} \right)}}{2} \right)}\right) - \sqrt[4]{\left(1 - \operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(x\right)},1 - \operatorname{re}{\left(x\right)} \right)}}{2} \right)} \approx - i \left(\left(1.0 - \operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{0.25} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(x\right)},1 - \operatorname{re}{\left(x\right)} \right)}}{2} \right)} - \left(\left(1.0 - \operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{0.25} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(x\right)},1 - \operatorname{re}{\left(x\right)} \right)}}{2} \right)}\]

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