What is the answer to x^2+(2-2i)x-(4+2x)=0 ?

The answer to x^2+(2-2i)x-(4+2x)=0 is x=sqrt(3)+i,x=-sqrt(3)+i

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

x^2+(2-2i)x-(4+2x)=0

x^{2} + (2 - 2 i) x - (4 + 2 x) = 0

x = 3 + i, x = - 3 + i

Solution steps

x^{2} + (2 - 2 i) x - (4 + 2 x) = 0

Substitute

x = a + bi

(a + bi)^{2} + (2 - 2 i) (a + bi) - (4 + 2 (a + bi)) = 0

Expand

(a + bi)^{2} + (2 - 2 i) (a + bi) - (4 + 2 (a + bi)) : (a^{2} - b^{2} + 2 b - 4) + i (- 2 a + 2 ab)

(a^{2} - b^{2} + 2 b - 4) + i (- 2 a + 2 ab) = 0

Rewrite

0

in standard complex form:

0 + 0 i

(a^{2} - b^{2} + 2 b - 4) + i (- 2 a + 2 ab) = 0 + 0 i

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

[a^{2} - b^{2} + 2 b - 4 = 0 - 2 a + 2 ab = 0]

[a^{2} - b^{2} + 2 b - 4 = 0 - 2 a + 2 ab = 0] : (a = 3, a = - 3, b = 1 b = 1)

Substitute back

x = a + bi

x = 3 + i, x = - 3 + i

2 x - 20 i = 8 - (4 y) i

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

aa - 2 a - 3 i = 0

x - y i = - 2 + 3 i

\frac{1}{2 - i} = a + ib

What is the answer to x^2+(2-2i)x-(4+2x)=0 ?
The answer to x^2+(2-2i)x-(4+2x)=0 is x=sqrt(3)+i,x=-sqrt(3)+i