Issolvi i(1+4i)^3/(3-2i)^2

$$\frac { i ( 1 + 4 i ) ^ { 3 } } { ( 3 - 2 i ) ^ { 2 } }$$

Evalwa

$$\frac{824}{169}+\frac{389}{169}i\approx 4.875739645+2.301775148i$$

Passi tas-Soluzzjonijiet

Ikkalkula 1+4i bil-power ta' 3 u tikseb -47-52i.

$$\frac{i\left(-47-52i\right)}{\left(3-2i\right)^{2}}$$

Immultiplika i u -47-52i biex tikseb 52-47i.

$$\frac{52-47i}{\left(3-2i\right)^{2}}$$

Ikkalkula 3-2i bil-power ta' 2 u tikseb 5-12i.

$$\frac{52-47i}{5-12i}$$

Immultiplika kemm in-numeratur u d-denominatur bil-konjugat kumpless tad-denominatur, 5+12i.

$$\frac{\left(52-47i\right)\left(5+12i\right)}{\left(5-12i\right)\left(5+12i\right)}$$

Agħmel il-multiplikazzjonijiet fi \frac{\left(52-47i\right)\left(5+12i\right)}{\left(5-12i\right)\left(5+12i\right)}.

$$\frac{824+389i}{169}$$

Iddividi 824+389i b'169 biex tikseb\frac{824}{169}+\frac{389}{169}i.

$$\frac{824}{169}+\frac{389}{169}i$$

Parti Reali

$$\frac{824}{169} = 4\frac{148}{169} = 4.875739644970414$$

Passi tas-Soluzzjonijiet

Ikkalkula 1+4i bil-power ta' 3 u tikseb -47-52i.

$$Re(\frac{i\left(-47-52i\right)}{\left(3-2i\right)^{2}})$$

Immultiplika i u -47-52i biex tikseb 52-47i.

$$Re(\frac{52-47i}{\left(3-2i\right)^{2}})$$

Ikkalkula 3-2i bil-power ta' 2 u tikseb 5-12i.

$$Re(\frac{52-47i}{5-12i})$$

Immultiplika kemm in-numeratur u d-denominatur ta' \frac{52-47i}{5-12i} bil-konjugat kumpless tad-denominatur, 5+12i.

$$Re(\frac{\left(52-47i\right)\left(5+12i\right)}{\left(5-12i\right)\left(5+12i\right)})$$

Agħmel il-multiplikazzjonijiet fi \frac{\left(52-47i\right)\left(5+12i\right)}{\left(5-12i\right)\left(5+12i\right)}.

$$Re(\frac{824+389i}{169})$$

Iddividi 824+389i b'169 biex tikseb\frac{824}{169}+\frac{389}{169}i.

$$Re(\frac{824}{169}+\frac{389}{169}i)$$

Il-parti reali ta' \frac{824}{169}+\frac{389}{169}i hija \frac{824}{169}.

$$\frac{824}{169}$$