What is the answer to solvefor m,r=(i-m)/(1+m) ?

The answer to solvefor m,r=(i-m)/(1+m) is m=-r/(r+1)+1/(r+1)i

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solvefor m,r=(i-m)/(1+m)

solve for

m, r = \frac{i - m}{1 + m}

m = - \frac{r}{r + 1} + \frac{1}{r + 1} i

Solution steps

r = \frac{i - m}{1 + m}

Substitute

m = x + y i

r = \frac{i - ( x + y i )}{1 + x + y i}

Multiply both sides by

1 + x + i y

r (1 + x + i y) = \frac{i - ( x + y i )}{1 + x + y i} (1 + x + i y)

Expand

r + r x + i ry = - x + i (1 - y)

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

[r + r x = - x ry = 1 - y]

[r + r x = - x ry = 1 - y] : x = - \frac{r}{r + 1}, y = \frac{1}{r + 1}, r \neq = - 1

Substitute back

m = x + y i

m = - \frac{r}{r + 1} + \frac{1}{r + 1} i

- 9 x + 8 i = - 54 + (16 y) i

x^{2} - (2 - 4 i) x - (3 + 6 i) = 0

y - 8 = 3 (x + 1) in

x, R s i R (x) = 8 - 2 x + x^{2}

3 x - 200 s i \cdot = - 10

What is the answer to solvefor m,r=(i-m)/(1+m) ?
The answer to solvefor m,r=(i-m)/(1+m) is m=-r/(r+1)+1/(r+1)i