What is the answer to (2z}{1+i^9}-\frac{2z)/i = 5/(2-i^7) ?

The answer to (2z}{1+i^9}-\frac{2z)/i = 5/(2-i^7) is z= 1/2-i 3/2

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(2z}{1+i^9}-\frac{2z)/i = 5/(2-i^7)

\frac{2 z}{1 + i ^{9}} - \frac{2 z}{i} = \frac{5}{2 - i ^{7}}

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

Solution steps

\frac{2 z}{1 + i ^{9}} - \frac{2 z}{i} = \frac{5}{2 - i ^{7}}

Simplify

\frac{2 z}{1 + i ^{9}} - \frac{2 z}{i} : \frac{2 z}{1 + i} - \frac{2 z}{i}

Simplify

\frac{5}{2 - i ^{7}} : \frac{5}{2 + i}

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

Multiply by LCM

2 i (2 + i) z - 2 (1 + i) (2 + i) z = 5 i (1 + i)

Expand

2 i (2 + i) z - 2 (1 + i) (2 + i) z : - 2 i z - 4 z

Expand

5 i (1 + i) : - 5 + 5 i

- 2 i z - 4 z = - 5 + 5 i

Factor

- 2 i z - 4 z : - 2 (i + 2) z

- 2 (i + 2) z = - 5 + 5 i

Divide both sides by

- 2 (i + 2)

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

4 (- 7) - 5 (- 3) = - 13

y = 2 (2)

1.5 p - 9 = - 3

2 + 8 (7 + x) = 82

lo g_{5} (\frac{1}{5}) = x

What is the answer to (2z}{1+i^9}-\frac{2z)/i = 5/(2-i^7) ?
The answer to (2z}{1+i^9}-\frac{2z)/i = 5/(2-i^7) is z= 1/2-i 3/2