en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify (2+i)/(3-i)

Solution

simplify

\frac{2 + i}{3 - i}

Solution

\frac{1}{2} + \frac{1}{2} i

Solution steps

\frac{2 + i}{3 - i}

Multiply by the conjugate

\frac{3 + i}{3 + i}

= \frac{( 2 + i ) ( 3 + i )}{( 3 - i ) ( 3 + i )}

Simplify

\frac{( 2 + i ) ( 3 + i )}{( 3 - i ) ( 3 + i )} : \frac{5 + 5 i}{10}

= \frac{5 + 5 i}{10}

Apply the fraction rule:

\frac{a + bi}{c} = \frac{a}{c} + \frac{b}{c} i

= \frac{5}{10} + \frac{5}{10} i

Simplify

\frac{5}{10} + \frac{5}{10} i : \frac{1}{2} + \frac{1}{2} i

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

Popular Examples

x^{2} - 20 x + 64 = 0

9x-2<7\land 3x-5>10

9 x - 2 < 7 and 3 x - 5 > 10

factor 3x^2y+4xy^2 factor

3 x^{2} y + 4 x y^{2}

simplify a^7a^4 simplify

a^{7} a^{4}

x+13<=-1/2 \lor x+13>= 1/2

x + 13 \leq - \frac{1}{2} or x + 13 \geq \frac{1}{2}

Frequently Asked Questions (FAQ)

What is (2+i)/(3-i) ?
The solution to (2+i)/(3-i) is 1/2+1/2 i