y $^{4}$ = 2
find y
You asked:
Solve the equation \[{y}^{4} = 2\] for the unknown \(y\).
MathBot Answer:
The solutions are given by the formula: \[y = \sqrt[4]{2} \cos{\left(\frac{\pi k}{2} \right)} + \sqrt[4]{2} \sin{\left(\frac{\pi k}{2} \right)} i\] where \(k\) is an integer in \(0 \le k < 4\).
There are \(2\) real solutions.
There are \(2\) solutions with nonzero imaginary part.
Real solutions: \[\begin{aligned}y &= \sqrt[4]{2} \\&\approx 1.1892071\\y &= - \sqrt[4]{2} \\&\approx -1.1892071\end{aligned}\]
Solutions with nonzero imaginary part: \[\begin{aligned}y &= \sqrt[4]{2} i \\&\approx 1.1892071 i\\y &= - \sqrt[4]{2} i \\&\approx -1.1892071 i\end{aligned}\]
\(i\) is the imaginary unit, defined as \(i^2 = -1\).