Assuming the 9090 was meant to be in degrees:
e^(90^circi) = cos(90^circ)+i * sin(90^circ)color(white)("xxxx")e90∘i=cos(90∘)+i⋅sin(90∘)xxxx[Euler's formula]
Using De Moivre's formula
sqrt(cos(90^circ)+i * sin(90^circ))=+-[cos(45^circ)+i * sin(45^circ)]√cos(90∘)+i⋅sin(90∘)=±[cos(45∘)+i⋅sin(45∘)]
root(4)(e^(90^circ)i)=sqrt(+-[cos(45^circ)+i * sin(45^circ)])4√e90∘i=√±[cos(45∘)+i⋅sin(45∘)]
Re-applying deMoivre's formula
{:
(sqrt(+[cos(45^circ)+i * sin(45^circ)]),color(white)("xx"),sqrt(-[cos(45^circ)+i * sin(45^circ)])),
(=+-[cos(22.5^circ)+i * sin(22.5^circ)],,=+-i * [cos(22.5^circ)+i * sin(22.5^circ)]),
(,,=+-[i *cos(22.5^circ)-sin(22.5^circ)])
:}
For approximate values you could substitute the approximations:
{:(cos(22.5^circ)~~0.9239,color(white)("xx")sin(22.5^circ)~~0.3827):}
