What is the answer to i(x)=(4x+2)/(2x+1) ?

The answer to i(x)=(4x+2)/(2x+1) is x=-2i,x=-1/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

i(x)=(4x+2)/(2x+1)

i (x) = \frac{4 x + 2}{2 x + 1}

x = - 2 i, x = - \frac{1}{2}

Solution steps

i (x) = \frac{4 x + 2}{2 x + 1}

Substitute

x = a + bi

i (a + bi) = \frac{4 ( a + bi ) + 2}{2 ( a + bi ) + 1}

Multiply both sides by

2 a + 1 + 2 ib

i (a + bi) (2 a + 1 + 2 ib) = \frac{4 ( a + bi ) + 2}{2 ( a + bi ) + 1} (2 a + 1 + 2 ib)

Expand

(- 4 ab - b) + i (a + 2 a^{2} - 2 b^{2}) = (4 a + 2) + 4 ib

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

[- 4 ab - b = 4 a + 2 a + 2 a^{2} - 2 b^{2} = 4 b]

[- 4 ab - b = 4 a + 2 a + 2 a^{2} - 2 b^{2} = 4 b] : (a = 0, a = - \frac{1}{2}, b = - 2 b = 0)

Substitute back

x = a + bi

x = - 2 i, x = - \frac{1}{2}

- \frac{6}{5} w = 9

\frac{5}{8} (16 d + 24) = 6 (d - 1) + 1

- 3 = \frac{y}{7}

2 x + 7 = 4 (x - 3)

- 5 d + 4 = 12

What is the answer to i(x)=(4x+2)/(2x+1) ?
The answer to i(x)=(4x+2)/(2x+1) is x=-2i,x=-1/2