What is the answer to (x+iy)/(1+(x-iy))=3+4i ?

The answer to (x+iy)/(1+(x-iy))=3+4i is x=-7/6 ,y=-1/6

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(x+iy)/(1+(x-iy))=3+4i

\frac{x + i y}{1 + ( x - i y )} = 3 + 4 i

x = - \frac{7}{6}, y = - \frac{1}{6}

Solution steps

\frac{x + i y}{1 + ( x - i y )} = 3 + 4 i

Multiply both sides by

1 + x - i y

\frac{x + i y}{1 + x - i y} (1 + x - i y) = 3 (1 + x - i y) + 4 i (1 + x - i y)

Expand

x + i y = (3 + 3 x + 4 y) + i (4 - 3 y + 4 x)

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

[x = 3 + 3 x + 4 y y = 4 - 3 y + 4 x]

[x = 3 + 3 x + 4 y y = 4 - 3 y + 4 x] : x = - \frac{7}{6}, y = - \frac{1}{6}

x = - \frac{7}{6}, y = - \frac{1}{6}

(i - 5) z + (i - 2) z^{2} + 2 - 2 i = 0

z - \frac{1}{z} = 3 + 4 i

i (x) = ∣ 2 y + 5 ∣

(a + bi)^{2} + 2 (a - bi) + 1 = 0

m, y = (x - 3)^{2} minim o

What is the answer to (x+iy)/(1+(x-iy))=3+4i ?
The answer to (x+iy)/(1+(x-iy))=3+4i is x=-7/6 ,y=-1/6