Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[({u}^{2}+{u}^{2})\imath =100\]
Simplify \({u}^{2}+{u}^{2}\) to \(2{u}^{2}\).
\[2{u}^{2}\imath =100\]
Regroup terms.
\[2\imath {u}^{2}=100\]
Divide both sides by \(2\).
\[\imath {u}^{2}=\frac{100}{2}\]
Simplify \(\frac{100}{2}\) to \(50\).
\[\imath {u}^{2}=50\]
Divide both sides by \(\imath \).
\[{u}^{2}=\frac{50}{\imath }\]
Rationalize the denominator: \(\frac{50}{\imath } \cdot \frac{\imath }{\imath }=-50\imath \).
\[{u}^{2}=-50\imath \]
Take the square root of both sides.
\[u=\pm \sqrt{-50\imath }\]
Simplify \(\sqrt{-50\imath }\) to \(\sqrt{50\imath }\imath \).
\[u=\pm \sqrt{50\imath }\imath \]
Use this rule: \(\sqrt{ab}=\sqrt{a}\sqrt{b}\).
\[u=\pm \sqrt{50}\sqrt{\imath }\imath \]
Simplify \(\sqrt{50}\) to \(5\sqrt{2}\).
\[u=\pm 5\sqrt{2}\sqrt{\imath }\imath \]
Simplify \(5\sqrt{2}\sqrt{\imath }\imath \) to \(5\sqrt{2\imath }\imath \).
\[u=\pm 5\sqrt{2\imath }\imath \]
u=5*sqrt(2*IM)*IM,-5*sqrt(2*IM)*IM
