Issolvi frac{1^{80}+i^{12}-3i^26+2i^14}{9+2i-1^35*1^9}

$$\frac { 1 ^ { 80 } + i ^ { 12 } - 3 i ^ { 26 } + 2 i ^ { 14 } } { 9 + 2 i - 1 ^ { 35 } \cdot 1 ^ { 9 } }$$

Evalwa

$$\frac{6}{17}-\frac{3}{34}i\approx 0.352941176-0.088235294i$$

Passi tas-Soluzzjonijiet

Biex timmultiplika l-qawwa tal-istess bażi, żid l-esponenti tagħhom. Żid 35 u 9 biex tikseb 44.

$$\frac{1^{80}+i^{12}-3i^{26}+2i^{14}}{9+2i-1^{44}}$$

Ikkalkula 1 bil-power ta' 80 u tikseb 1.

$$\frac{1+i^{12}-3i^{26}+2i^{14}}{9+2i-1^{44}}$$

Ikkalkula i bil-power ta' 12 u tikseb 1.

$$\frac{1+1-3i^{26}+2i^{14}}{9+2i-1^{44}}$$

Żid 1 u 1 biex tikseb 2.

$$\frac{2-3i^{26}+2i^{14}}{9+2i-1^{44}}$$

Ikkalkula i bil-power ta' 26 u tikseb -1.

$$\frac{2-3\left(-1\right)+2i^{14}}{9+2i-1^{44}}$$

Immultiplika 3 u -1 biex tikseb -3.

$$\frac{2-\left(-3\right)+2i^{14}}{9+2i-1^{44}}$$

L-oppost ta' -3 huwa 3.

$$\frac{2+3+2i^{14}}{9+2i-1^{44}}$$

Żid 2 u 3 biex tikseb 5.

$$\frac{5+2i^{14}}{9+2i-1^{44}}$$

Ikkalkula i bil-power ta' 14 u tikseb -1.

$$\frac{5+2\left(-1\right)}{9+2i-1^{44}}$$

Immultiplika 2 u -1 biex tikseb -2.

$$\frac{5-2}{9+2i-1^{44}}$$

Naqqas 2 minn 5 biex tikseb 3.

$$\frac{3}{9+2i-1^{44}}$$

Ikkalkula 1 bil-power ta' 44 u tikseb 1.

$$\frac{3}{9+2i-1}$$

Naqqas 1 minn 9+2i biex tikseb 8+2i.

$$\frac{3}{8+2i}$$

Immultiplika kemm in-numeratur u d-denominatur bil-konjugat kumpless tad-denominatur, 8-2i.

$$\frac{3\left(8-2i\right)}{\left(8+2i\right)\left(8-2i\right)}$$

Agħmel il-multiplikazzjonijiet fi \frac{3\left(8-2i\right)}{\left(8+2i\right)\left(8-2i\right)}.

$$\frac{24-6i}{68}$$

Iddividi 24-6i b'68 biex tikseb\frac{6}{17}-\frac{3}{34}i.

$$\frac{6}{17}-\frac{3}{34}i$$

Parti Reali

$$\frac{6}{17} = 0.35294117647058826$$

Passi tas-Soluzzjonijiet

Biex timmultiplika l-qawwa tal-istess bażi, żid l-esponenti tagħhom. Żid 35 u 9 biex tikseb 44.

$$Re(\frac{1^{80}+i^{12}-3i^{26}+2i^{14}}{9+2i-1^{44}})$$

Ikkalkula 1 bil-power ta' 80 u tikseb 1.

$$Re(\frac{1+i^{12}-3i^{26}+2i^{14}}{9+2i-1^{44}})$$

Ikkalkula i bil-power ta' 12 u tikseb 1.

$$Re(\frac{1+1-3i^{26}+2i^{14}}{9+2i-1^{44}})$$

Żid 1 u 1 biex tikseb 2.

$$Re(\frac{2-3i^{26}+2i^{14}}{9+2i-1^{44}})$$

Ikkalkula i bil-power ta' 26 u tikseb -1.

$$Re(\frac{2-3\left(-1\right)+2i^{14}}{9+2i-1^{44}})$$

Immultiplika 3 u -1 biex tikseb -3.

$$Re(\frac{2-\left(-3\right)+2i^{14}}{9+2i-1^{44}})$$

L-oppost ta' -3 huwa 3.

$$Re(\frac{2+3+2i^{14}}{9+2i-1^{44}})$$

Żid 2 u 3 biex tikseb 5.

$$Re(\frac{5+2i^{14}}{9+2i-1^{44}})$$

Ikkalkula i bil-power ta' 14 u tikseb -1.

$$Re(\frac{5+2\left(-1\right)}{9+2i-1^{44}})$$

Immultiplika 2 u -1 biex tikseb -2.

$$Re(\frac{5-2}{9+2i-1^{44}})$$

Naqqas 2 minn 5 biex tikseb 3.

$$Re(\frac{3}{9+2i-1^{44}})$$

Ikkalkula 1 bil-power ta' 44 u tikseb 1.

$$Re(\frac{3}{9+2i-1})$$

Naqqas 1 minn 9+2i biex tikseb 8+2i.

$$Re(\frac{3}{8+2i})$$

Immultiplika kemm in-numeratur u d-denominatur ta' \frac{3}{8+2i} bil-konjugat kumpless tad-denominatur, 8-2i.

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

Agħmel il-multiplikazzjonijiet fi \frac{3\left(8-2i\right)}{\left(8+2i\right)\left(8-2i\right)}.

$$Re(\frac{24-6i}{68})$$

Iddividi 24-6i b'68 biex tikseb\frac{6}{17}-\frac{3}{34}i.

$$Re(\frac{6}{17}-\frac{3}{34}i)$$

Il-parti reali ta' \frac{6}{17}-\frac{3}{34}i hija \frac{6}{17}.

$$\frac{6}{17}$$