Riješi 8+3i/-9+4iquad(-9-7)

$$\frac { 8 + 3 i } { - 9 + 4 i } \quad ( - 9 - 7 )$$

Izračunaj

$$\frac{960}{97}+\frac{944}{97}i\approx 9,896907216+9,731958763i$$

Koraci rješenja

Pomnožite brojnik i nazivnik izraza \frac{8+3i}{-9+4i} s kompleksnim konjugatom nazivnika, -9-4i.

$$\frac{\left(8+3i\right)\left(-9-4i\right)}{\left(-9+4i\right)\left(-9-4i\right)}\left(-9-7\right)$$

Umnožak se može pretvoriti u razliku kvadrata pomoću sljedećeg pravila: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{\left(8+3i\right)\left(-9-4i\right)}{\left(-9\right)^{2}-4^{2}i^{2}}\left(-9-7\right)$$

Prema definiciji: i^{2} jednako -1. Izračunajte nazivnik.

$$\frac{\left(8+3i\right)\left(-9-4i\right)}{97}\left(-9-7\right)$$

Kompleksne brojeve 8+3i i -9-4i množite kao što biste množili binome.

$$\frac{8\left(-9\right)+8\times \left(-4i\right)+3i\left(-9\right)+3\left(-4\right)i^{2}}{97}\left(-9-7\right)$$

Prema definiciji: i^{2} jednako -1.

$$\frac{8\left(-9\right)+8\times \left(-4i\right)+3i\left(-9\right)+3\left(-4\right)\left(-1\right)}{97}\left(-9-7\right)$$

Pomnožite izraz 8\left(-9\right)+8\times \left(-4i\right)+3i\left(-9\right)+3\left(-4\right)\left(-1\right).

$$\frac{-72-32i-27i+12}{97}\left(-9-7\right)$$

Kombinirajte realne i imaginarne dijelove u izrazu -72-32i-27i+12.

$$\frac{-72+12+\left(-32-27\right)i}{97}\left(-9-7\right)$$

Zbrojite izraz -72+12+\left(-32-27\right)i.

$$\frac{-60-59i}{97}\left(-9-7\right)$$

Podijelite -60-59i s 97 da biste dobili -\frac{60}{97}-\frac{59}{97}i.

$$\left(-\frac{60}{97}-\frac{59}{97}i\right)\left(-9-7\right)$$

Oduzmite 7 od -9 da biste dobili -16.

$$\left(-\frac{60}{97}-\frac{59}{97}i\right)\left(-16\right)$$

Pomnožite -\frac{60}{97}-\frac{59}{97}i i -16.

$$-\frac{60}{97}\left(-16\right)-\frac{59}{97}i\left(-16\right)$$

Pomnožite.

$$\frac{960}{97}+\frac{944}{97}i$$

Realni dio

$$\frac{960}{97} = 9\frac{87}{97} = 9,896907216494846$$

Koraci rješenja

Pomnožite brojnik i nazivnik izraza \frac{8+3i}{-9+4i} s kompleksnim konjugatom nazivnika, -9-4i.

$$Re(\frac{\left(8+3i\right)\left(-9-4i\right)}{\left(-9+4i\right)\left(-9-4i\right)}\left(-9-7\right))$$

Umnožak se može pretvoriti u razliku kvadrata pomoću sljedećeg pravila: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$Re(\frac{\left(8+3i\right)\left(-9-4i\right)}{\left(-9\right)^{2}-4^{2}i^{2}}\left(-9-7\right))$$

Prema definiciji: i^{2} jednako -1. Izračunajte nazivnik.

$$Re(\frac{\left(8+3i\right)\left(-9-4i\right)}{97}\left(-9-7\right))$$

Kompleksne brojeve 8+3i i -9-4i množite kao što biste množili binome.

$$Re(\frac{8\left(-9\right)+8\times \left(-4i\right)+3i\left(-9\right)+3\left(-4\right)i^{2}}{97}\left(-9-7\right))$$

Prema definiciji: i^{2} jednako -1.

$$Re(\frac{8\left(-9\right)+8\times \left(-4i\right)+3i\left(-9\right)+3\left(-4\right)\left(-1\right)}{97}\left(-9-7\right))$$

Pomnožite izraz 8\left(-9\right)+8\times \left(-4i\right)+3i\left(-9\right)+3\left(-4\right)\left(-1\right).

$$Re(\frac{-72-32i-27i+12}{97}\left(-9-7\right))$$

Kombinirajte realne i imaginarne dijelove u izrazu -72-32i-27i+12.

$$Re(\frac{-72+12+\left(-32-27\right)i}{97}\left(-9-7\right))$$

Zbrojite izraz -72+12+\left(-32-27\right)i.

$$Re(\frac{-60-59i}{97}\left(-9-7\right))$$

Podijelite -60-59i s 97 da biste dobili -\frac{60}{97}-\frac{59}{97}i.

$$Re(\left(-\frac{60}{97}-\frac{59}{97}i\right)\left(-9-7\right))$$

Oduzmite 7 od -9 da biste dobili -16.

$$Re(\left(-\frac{60}{97}-\frac{59}{97}i\right)\left(-16\right))$$

Pomnožite -\frac{60}{97}-\frac{59}{97}i i -16.

$$Re(-\frac{60}{97}\left(-16\right)-\frac{59}{97}i\left(-16\right))$$

Pomnožite izraz -\frac{60}{97}\left(-16\right)-\frac{59}{97}i\left(-16\right).

$$Re(\frac{960}{97}+\frac{944}{97}i)$$

Realni dio broja \frac{960}{97}+\frac{944}{97}i jest \frac{960}{97}.

$$\frac{960}{97}$$