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

Lösung

erweitern

\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}

Schritte zur Lösung

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

Multipliziere aus

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

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

Rationalisiere

\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}

Schreibe

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

in der Standard komplexen Form um:

\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

e x p an d 2 (ln (x))

e x p an d \frac{( s + 2 )}{( 5 s + 3 ) ^{\frac{3}{2}}}

e x p an d 6 (g) + 8

e x p an d \frac{2 x - s ^{2} - 1}{s ^{2} ( s ^{2} + 4 ) ( 2 s - 1 )}

e x p an d 4 sin (4 (x - 45))