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

The answer to (1+i)/z-(1+2i)=i is z= 2/5-1/5 i

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(1+i)/z-(1+2i)=i

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

z = \frac{2}{5} - \frac{1}{5} i

Solution steps

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

Substitute

z = x + y i

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

Multiply both sides by

x + y i

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

Expand

(1 - x + 2 y) + i (1 - y - 2 x) = - y + i x

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

[1 - x + 2 y = - y 1 - y - 2 x = x]

[1 - x + 2 y = - y 1 - y - 2 x = x] : x = \frac{2}{5}, y = - \frac{1}{5}

Substitute back

z = x + y i

z = \frac{2}{5} - \frac{1}{5} i

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

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

2 z^{2} - 7 z + 4 = i (2 z + 1)

x + 2 + 7 i = y i - 2

i (x) = - x^{2} + 80 x + 650

What is the answer to (1+i)/z-(1+2i)=i ?
The answer to (1+i)/z-(1+2i)=i is z= 2/5-1/5 i