What is the answer to 0.005xi= 1/(0.000018xi) ?

The answer to 0.005xi= 1/(0.000018xi) is x= 10000/3 i,x=-10000/3 i

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

0.005xi= 1/(0.000018xi)

0.005 x i = \frac{1}{0.000018 x i}

x = \frac{10000}{3} i, x = - \frac{10000}{3} i

Solution steps

0.005 x i = \frac{1}{0.000018 x i}

Substitute

x = a + bi

0.005 (a + bi) i = \frac{1}{0.000018 ( a + bi ) i}

Multiply both sides by

0.000018 (a + bi) i

0.005 (a + bi) i 0.000018 (a + bi) i = \frac{1}{0.000018 ( a + bi ) i} \cdot 0.000018 (a + bi) i

Expand

(- 0.00000009 a^{2} + 0.00000009 b^{2}) - 0.00000018 iab = 1

Rewrite

1

in standard complex form:

1 + 0 i

(- 0.00000009 a^{2} + 0.00000009 b^{2}) - 0.00000018 iab = 1 + 0 i

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

[- 0.00000009 a^{2} + 0.00000009 b^{2} = 1 - 0.00000018 ab = 0]

[- 0.00000009 a^{2} + 0.00000009 b^{2} = 1 - 0.00000018 ab = 0] : (a = 0, a = 0, b = \frac{10000}{3} b = - \frac{10000}{3})

Substitute back

x = a + bi

x = \frac{10000}{3} i, x = - \frac{10000}{3} i

z^{2} - (3 + 6 i) z - 4 - 6 i = 0

i (x + i y) = x + i + i 2 y

4 - i x = y - 3 i

a^{2} i - b^{2} i = - a^{2} + b^{2} i l

4 = \frac{x}{2} + \frac{x - y}{8 + 6 i}

What is the answer to 0.005xi= 1/(0.000018xi) ?
The answer to 0.005xi= 1/(0.000018xi) is x= 10000/3 i,x=-10000/3 i