What is the answer to z/2+(1-i)/(2+i)z-i=3 ?

The answer to z/2+(1-i)/(2+i)z-i=3 is z= 30/17+i 50/17

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z/2+(1-i)/(2+i)z-i=3

\frac{z}{2} + \frac{1 - i}{2 + i} z - i = 3

z = \frac{30}{17} + i \frac{50}{17}

Solution steps

\frac{z}{2} + \frac{1 - i}{2 + i} z - i = 3

\frac{1 - i}{2 + i} = \frac{1 - 3 i}{5}

\frac{z}{2} + \frac{1 - 3 i}{5} z - i = 3

Move

i

to the right side

\frac{z}{2} + \frac{1 - 3 i}{5} z = 3 + i

Multiply by LCM

5 z + 2 (1 - 3 i) z = 30 + 10 i

Expand

2 z (1 - 3 i) : 2 z - 6 i z

5 z + 2 z - 6 i z = 30 + 10 i

Add similar elements:

5 z + 2 z = 7 z

7 z - 6 i z = 30 + 10 i

Factor

7 z - 6 i z : (7 - 6 i) z

(7 - 6 i) z = 30 + 10 i

Divide both sides by

7 - 6 i

z = \frac{30}{17} + i \frac{50}{17}

n^{2} - 2 n - 8

1 = 3

x + 1 = 16 (- x - 1)

x + \frac{x}{2} + 4 = 71

f = 3 (2)^{- 1}

What is the answer to z/2+(1-i)/(2+i)z-i=3 ?
The answer to z/2+(1-i)/(2+i)z-i=3 is z= 30/17+i 50/17