Solve fi=ni/Nquadfjn/N

$$f i = \frac { n i } { N } \quad f j \frac { n } { N }$$

Solve for f

$$\left\{\begin{matrix}f=0\text{, }&N\neq 0\\f\in \mathrm{C}\text{, }&\left(n=-j^{-\frac{1}{2}}N\text{ or }n=j^{-\frac{1}{2}}N\right)\text{ and }j\neq 0\text{ and }N\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by N.

$$fiN=nifj\times \frac{n}{N}$$

Express n\times \frac{n}{N} as a single fraction.

$$fiN=\frac{nn}{N}ifj$$

Multiply n and n to get n^{2}.

$$fiN=\frac{n^{2}}{N}ifj$$

Express \frac{n^{2}}{N}f as a single fraction.

$$fiN=\frac{n^{2}f}{N}ij$$

Express \frac{n^{2}f}{N}j as a single fraction.

$$fiN=\frac{n^{2}fj}{N}i$$

Subtract \frac{n^{2}fj}{N}i from both sides.

$$fiN-\frac{n^{2}fj}{N}i=0$$

Multiply both sides of the equation by N.

$$fiNN-n^{2}fji=0$$

Reorder the terms.

$$iNNf-ifjn^{2}=0$$

Multiply N and N to get N^{2}.

$$iN^{2}f-ifjn^{2}=0$$

Combine all terms containing f.

$$\left(iN^{2}-ijn^{2}\right)f=0$$

Divide 0 by iN^{2}-ijn^{2}.

$$f=0$$

Solve for N

$$\left\{\begin{matrix}N=-\sqrt{j}n\text{; }N=\sqrt{j}n\text{, }&j\neq 0\text{ and }n\neq 0\\N\neq 0\text{, }&f=0\end{matrix}\right.$$