What is the answer to 0=z+i/z ?

The answer to 0=z+i/z is z= 1/(sqrt(2))-1/(sqrt(2))i,z=-1/(sqrt(2))+1/(sqrt(2))i

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0=z+i/z

0 = z + \frac{i}{z}

z = \frac{1}{2} - \frac{1}{2} i, z = - \frac{1}{2} + \frac{1}{2} i

Solution steps

0 = z + \frac{i}{z}

Substitute

z = x + y i

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

Multiply both sides by

x + y i

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

Expand

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

Rewrite

0

in standard complex form:

0 + 0 i

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

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

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

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

Substitute back

z = x + y i

z = \frac{1}{2} - \frac{1}{2} i, z = - \frac{1}{2} + \frac{1}{2} i

15 - 28 = 3 l + (4 m) i

+ 4 i z^{2} = 2 + 2 i, z^{1} = 7

\frac{2 + ai}{7 + bi} = 3 + 6 i

4 x + i (5 x - y) = 2 + i (- 3)

x, \frac{x}{1 - x} = 1 - 5 i

What is the answer to 0=z+i/z ?
The answer to 0=z+i/z is z= 1/(sqrt(2))-1/(sqrt(2))i,z=-1/(sqrt(2))+1/(sqrt(2))i