What is the answer to (i)x^2-16=0,(ii)6x^2-24=0 ?

The answer to (i)x^2-16=0,(ii)6x^2-24=0 is x=2sqrt(2)-2sqrt(2)i,x=-2sqrt(2)+2sqrt(2)i

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(i)x^2-16=0,(ii)6x^2-24=0

(i) x^{2} - 16 = 0, (ii) 6 x^{2} - 24 = 0

x = 22 - 22 i, x = - 22 + 22 i

Solution steps

(i) x^{2} - 16 = 0

Substitute

x = a + bi

i (a + bi)^{2} - 16 = 0

Expand

i (a + bi)^{2} - 16 : (- 2 ab - 16) + i (a^{2} - b^{2})

(- 2 ab - 16) + i (a^{2} - b^{2}) = 0

Rewrite

0

in standard complex form:

0 + 0 i

(- 2 ab - 16) + i (a^{2} - b^{2}) = 0 + 0 i

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

[- 2 ab - 16 = 0 a^{2} - b^{2} = 0]

[- 2 ab - 16 = 0 a^{2} - b^{2} = 0] : (a = 22, a = - 22, b = - 22 b = 22)

Substitute back

x = a + bi

x = 22 - 22 i, x = - 22 + 22 i

z^{2} + 3 z + 2 i = 0

(2 i + 1)^{2} = (m + ni) (2 - i)

2 (x - y i) + 5 (x + y i) + (x + y i)^{2} = 0

- 0.008 i = \frac{1}{x \cdot i}

M = C (1 + i)

What is the answer to (i)x^2-16=0,(ii)6x^2-24=0 ?
The answer to (i)x^2-16=0,(ii)6x^2-24=0 is x=2sqrt(2)-2sqrt(2)i,x=-2sqrt(2)+2sqrt(2)i