What is expand (6+8i)/(4+(x+3)i) ?

The solution to expand (6+8i)/(4+(x+3)i) is (48+8x)/(25+x^2+6x)+i(14-6x)/(25+x^2+6x)

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expand (6+8i)/(4+(x+3)i)

expand

\frac{6 + 8 i}{4 + ( x + 3 ) i}

\frac{48 + 8 x}{25 + x ^{2} + 6 x} + i \frac{14 - 6 x}{25 + x ^{2} + 6 x}

Solution steps

\frac{6 + 8 i}{4 + ( x + 3 ) i}

Expand

4 + (x + 3) i : 4 + i x + 3 i

= \frac{6 + 8 i}{4 + i x + 3 i}

Rationalize

\frac{6 + 8 i}{4 + i x + 3 i} : \frac{8 x + i ( - 6 x + 14 ) + 48}{x ^{2} + 6 x + 25}

= \frac{8 x + 48 + i ( - 6 x + 14 )}{x ^{2} + 6 x + 25}

Rewrite

\frac{8 x + 48 + i ( - 6 x + 14 )}{x ^{2} + 6 x + 25}

in standard complex form:

\frac{8 x + 48}{x ^{2} + 6 x + 25} + \frac{- 6 x + 14}{x ^{2} + 6 x + 25} i

= \frac{8 x + 48}{x ^{2} + 6 x + 25} + \frac{- 6 x + 14}{x ^{2} + 6 x + 25} i

2 (ln (x))

\frac{( s + 2 )}{( 5 s + 3 ) ^{\frac{3}{2}}}

6 (g) + 8

\frac{2 x - s ^{2} - 1}{s ^{2} ( s ^{2} + 4 ) ( 2 s - 1 )}

4 sin (4 (x - 45))

What is expand (6+8i)/(4+(x+3)i) ?
The solution to expand (6+8i)/(4+(x+3)i) is (48+8x)/(25+x^2+6x)+i(14-6x)/(25+x^2+6x)