What is factor (3+i)/(6+i) ?

The solution to factor (3+i)/(6+i) is 19/37+i 3/37

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

factor (3+i)/(6+i)

factor

\frac{3 + i}{6 + i}

\frac{19}{37} + i \frac{3}{37}

Solution steps

\frac{3 + i}{6 + i}

Apply complex arithmetic rule:

\frac{a + bi}{c + d i} = \frac{( c - d i ) ( a + bi )}{( c - d i ) ( c + d i )} = \frac{( a c + b d ) + ( b c - a d ) i}{c ^{2} + d ^{2}}

a = 3, b = 1, c = 6, d = 1

= \frac{( 3 \cdot 6 + 1 \cdot 1 ) + ( 1 \cdot 6 - 3 \cdot 1 ) i}{6 ^{2} + 1 ^{2}}

Refine

= \frac{19 + 3 i}{37}

Rewrite

\frac{19 + 3 i}{37}

in standard complex form:

\frac{19}{37} + \frac{3}{37} i

= \frac{19}{37} + \frac{3}{37} i

216 (x - 2)^{3} - (x - 1)^{3}

75 x^{2} - 7 x - 2 + 0

- r^{4} + 4 y^{3} + 21 y^{3}

x^{2} + x e^{3}

x^{2} + x^{2}