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

The answer to (1+i)/z-(4+3i)=i is z= 1/4

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(1+i)/z-(4+3i)=i

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

z = \frac{1}{4}

Decimal Notation

z = 0.25

Solution steps

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

Substitute

z = x + y i

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

Multiply both sides by

x + y i

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

Expand

(1 - 4 x + 3 y) + i (1 - 3 x - 4 y) = - y + i x

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

[1 - 4 x + 3 y = - y 1 - 3 x - 4 y = x]

[1 - 4 x + 3 y = - y 1 - 3 x - 4 y = x] : x = \frac{1}{4}, y = 0

Substitute back

z = x + y i

z = \frac{1}{4}

z^{2} - (5 + 2 i) z + 1 = 0

+ 6 i z^{2} = 3 + 5 i, z^{1} = 2

(2 + 3 i) (a + bi) = 13

22 (x + y i) + (28 + 4 i) = 72 - 62 i

a x^{2} - b x + 9 + 3 i = 0

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