What is the answer to z/(3+4i)+(2z+5i)/(1-2i)=2+2i ?

The answer to z/(3+4i)+(2z+5i)/(1-2i)=2+2i is z=4-3i

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

z/(3+4i)+(2z+5i)/(1-2i)=2+2i

\frac{z}{3 + 4 i} + \frac{2 z + 5 i}{1 - 2 i} = 2 + 2 i

z = 4 - 3 i

Solution steps

\frac{z}{3 + 4 i} + \frac{2 z + 5 i}{1 - 2 i} = 2 + 2 i

Multiply by LCM

(1 - 2 i) z + (3 + 4 i) (2 z + 5 i) = 2 (3 + 4 i) (1 - 2 i) + 2 i (3 + 4 i) (1 - 2 i)

Expand

(1 - 2 i) z + (3 + 4 i) (2 z + 5 i) : 6 i z + 7 z + 15 i - 20

Expand

2 (3 + 4 i) (1 - 2 i) + 2 i (3 + 4 i) (1 - 2 i) : 26 + 18 i

6 i z + 7 z + 15 i - 20 = 26 + 18 i

Move

15 i

to the right side

6 i z + 7 z - 20 = 26 + 3 i

Move

20

to the right side

6 i z + 7 z = 46 + 3 i

Factor

6 i z + 7 z : (6 i + 7) z

(6 i + 7) z = 46 + 3 i

Divide both sides by

6 i + 7

z = 4 - 3 i

x, 4 x + 3 y - 12 = 0

x, 3 x - y = 11

- 8 (2 m + 5) = 8

x, x + 5 y = - 15

y, 2 x + y = 3

What is the answer to z/(3+4i)+(2z+5i)/(1-2i)=2+2i ?
The answer to z/(3+4i)+(2z+5i)/(1-2i)=2+2i is z=4-3i