What is (3+i3)/(4+i6) ?

The solution to (3+i3)/(4+i6) is 15/26-3/26 i

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simplify (3+i3)/(4+i6)

simplify

\frac{3 + i 3}{4 + i 6}

\frac{15}{26} - \frac{3}{26} i

Solution steps

\frac{3 + i 3}{4 + i 6}

Rewrite

3 + i 3

in standard complex form:

3 + 3 i

Rewrite

4 + i 6

in standard complex form:

4 + 6 i

= \frac{3 + 3 i}{4 + 6 i}

Multiply by the conjugate

\frac{4 - 6 i}{4 - 6 i}

= \frac{( 3 + 3 i ) ( 4 - 6 i )}{( 4 + 6 i ) ( 4 - 6 i )}

Simplify

\frac{( 3 + 3 i ) ( 4 - 6 i )}{( 4 + 6 i ) ( 4 - 6 i )} : \frac{30 - 6 i}{52}

= \frac{30 - 6 i}{52}

Apply the fraction rule:

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

= \frac{30}{52} + \frac{- 6}{52} i

Simplify

\frac{30}{52} + \frac{- 6}{52} i : \frac{15}{26} - \frac{3}{26} i

= \frac{15}{26} - \frac{3}{26} i

(x - 4) (3 x + 4) = 0

\frac{x ^{2} - y ^{2}}{x ^{2} + 2 x y + y ^{2}}

\frac{x - 2}{x - 6} > 0

10 + 4 x = 5 (x - 6) + 33

x - 6 \geq 2