What is the answer to solvefor f,P=L+(si)/f ?

The answer to solvefor f,P=L+(si)/f is No Solution

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solvefor f,P=L+(si)/f

solve for

f, P = L + \frac{s i}{f}

No Solution

Solution steps

P = L + \frac{s i}{f}

Substitute

f = x + y i

P = L + \frac{s i}{x + y i}

Multiply both sides by

x + y i

P (x + y i) = L (x + y i) + \frac{s i}{x + y i} (x + y i)

Expand

P x + i P y = Lx + i (s + L y)

Complex numbers can be equal only if their real and imaginary parts are equalRewrite as system of equations:

[P x = Lx P y = s + L y]

[P x = Lx P y = s + L y] : No Solution

Substitute back

f = x + y i

No Solution

2 (x + i y) = i (2 + 9 i)

5 x + 13 + (2 y - 7) i = - 2 + i

x^{2} - 3 x + 3 + i = 0

(a + 5) + (b - 1) i = 7 - 3 i

z^{2} + 4 i z + 5 = 0

What is the answer to solvefor f,P=L+(si)/f ?
The answer to solvefor f,P=L+(si)/f is No Solution