What is the answer to x+iy+1/(x+iy)=0 ?

The answer to x+iy+1/(x+iy)=0 is

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x+iy+1/(x+iy)=0

x + i y + \frac{1}{x + i y} = 0

(x = 0, x = 0, y = 1 y = - 1)

Solution steps

x + i y + \frac{1}{x + i y} = 0

Multiply both sides by

x + i y

x (x + i y) + i y (x + i y) + \frac{1}{x + i y} (x + i y) = 0 \cdot (x + i y)

Expand

(x^{2} - y^{2} + 1) + 2 i x y = 0

Rewrite

0

in standard complex form:

0 + 0 i

(x^{2} - y^{2} + 1) + 2 i x y = 0 + 0 i

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

[x^{2} - y^{2} + 1 = 0 2 x y = 0]

[x^{2} - y^{2} + 1 = 0 2 x y = 0] : (x = 0, x = 0, y = 1 y = - 1)

(x = 0, x = 0, y = 1 y = - 1)

x (1 - x) = y^{2} - i y (2 x + 1)

(a^{2} - b^{2} - a + b) + (2 ab - b + a) i = 0

\frac{1 + i}{z} - (1 + 2 i) = i

f^{2} = \frac{1}{2} \cdot (f + i)

(x + 3) + 4 i = 2 + (y - 2) i