What is the answer to x^2=2+2sqrt(3)i ?

The answer to x^2=2+2sqrt(3)i 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+2sqrt(3)i

x^{2} = 2 + 23 i

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

Solution steps

x^{2} = 2 + 23 i

Substitute

x = a + bi

(a + bi)^{2} = 2 + 23 i

Expand

(a + bi)^{2} : (a^{2} - b^{2}) + 2 iab

(a^{2} - b^{2}) + 2 iab = 2 + 23 i

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

[a^{2} - b^{2} = 2 2 ab = 23]

[a^{2} - b^{2} = 2 2 ab = 23] : (a = 3, a = - 3, b = 1 b = - 1)

Substitute back

x = a + bi

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

z^{2} = 9 i

a + bi = 4

x^{2} = - 5 + 12 i

\frac{( x + y i )}{( x - y i )} = x - y i

\frac{100}{8 + 6 i} x + (1 - i)^{3} y = 7

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