What is the answer to (i/h)(4/3)=1 ?

The answer to (i/h)(4/3)=1 is h= 4/3 i

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(i/h)(4/3)=1

(\frac{i}{h}) (\frac{4}{3}) = 1

h = \frac{4}{3} i

Solution steps

(\frac{i}{h}) (\frac{4}{3}) = 1

Substitute

h = x + y i

\frac{i}{x + y i} \cdot \frac{4}{3} = 1

Multiply both sides by

3 x + 3 i y

\frac{i}{x + y i} \cdot \frac{4}{3} (3 x + 3 i y) = 1 \cdot (3 x + 3 i y)

Simplify

4 i = 3 x + 3 i y

Rewrite

4 i

in standard complex form:

0 + 4 i

0 + 4 i = 3 x + 3 i y

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

[0 = 3 x 4 = 3 y]

[0 = 3 x 4 = 3 y] : x = 0, y = \frac{4}{3}

Substitute back

h = x + y i

h = \frac{4}{3} i

x + y i = 2 + 3 i

x, (i (x - y))^{2} = 2

\frac{2 - i}{z - 1} = 2 + i

(x + y) + (x + y) i = 5 + 3 i

z^{2} - 2 i z - 1 = 0