$\sqrt{\-20y}$

asked by guest
on Jan 28, 2025 at 2:55 pm



You asked:

Evaluate the expression: (20y)\sqrt{-\left( 20 y \right)}

MathBot Answer:

Evaluated



(20y)=25y\displaystyle \sqrt{-\left( 20 y \right)} = 2 \sqrt{5} \sqrt{- y}


Roots

(20y)=i400(re(y))2+400(im(y))24sin(atan2(20im(y),20re(y))2)+400(re(y))2+400(im(y))24cos(atan2(20im(y),20re(y))2)4.47213595499958i((re(y))2+(im(y))2)0.25sin(atan2(20im(y),20re(y))2)+4.47213595499958((re(y))2+(im(y))2)0.25cos(atan2(20im(y),20re(y))2)\sqrt{-\left( 20 y \right)} = i \sqrt[4]{400 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 400 \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 20 \operatorname{im}{\left(y\right)},- 20 \operatorname{re}{\left(y\right)} \right)}}{2} \right)} + \sqrt[4]{400 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 400 \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 20 \operatorname{im}{\left(y\right)},- 20 \operatorname{re}{\left(y\right)} \right)}}{2} \right)} \approx 4.47213595499958 i \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{0.25} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 20 \operatorname{im}{\left(y\right)},- 20 \operatorname{re}{\left(y\right)} \right)}}{2} \right)} + 4.47213595499958 \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{0.25} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 20 \operatorname{im}{\left(y\right)},- 20 \operatorname{re}{\left(y\right)} \right)}}{2} \right)}(20y)=i(400(re(y))2+400(im(y))24sin(atan2(20im(y),20re(y))2))400(re(y))2+400(im(y))24cos(atan2(20im(y),20re(y))2)4.47213595499958i((re(y))2+(im(y))2)0.25sin(atan2(20im(y),20re(y))2)4.47213595499958((re(y))2+(im(y))2)0.25cos(atan2(20im(y),20re(y))2)\sqrt{-\left( 20 y \right)} = i \left(- \sqrt[4]{400 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 400 \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 20 \operatorname{im}{\left(y\right)},- 20 \operatorname{re}{\left(y\right)} \right)}}{2} \right)}\right) - \sqrt[4]{400 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 400 \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 20 \operatorname{im}{\left(y\right)},- 20 \operatorname{re}{\left(y\right)} \right)}}{2} \right)} \approx - 4.47213595499958 i \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{0.25} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 20 \operatorname{im}{\left(y\right)},- 20 \operatorname{re}{\left(y\right)} \right)}}{2} \right)} - 4.47213595499958 \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{0.25} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 20 \operatorname{im}{\left(y\right)},- 20 \operatorname{re}{\left(y\right)} \right)}}{2} \right)}