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

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

Aromātai

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

Ngā Upane Otinga

Hei whakarea i ngā pū o te pūtake kotahi, me tāpiri ō rātou taupū. Tāpiria te 35 me te 9 kia riro ai te 44.

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

Tātaihia te 1 mā te pū o 80, kia riro ko 1.

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

Tātaihia te i mā te pū o 12, kia riro ko 1.

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

Tāpirihia te 1 ki te 1, ka 2.

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

Tātaihia te i mā te pū o 26, kia riro ko -1.

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

Whakareatia te 3 ki te -1, ka -3.

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

Ko te tauaro o -3 ko 3.

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

Tāpirihia te 2 ki te 3, ka 5.

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

Tātaihia te i mā te pū o 14, kia riro ko -1.

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

Whakareatia te 2 ki te -1, ka -2.

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

Tangohia te 2 i te 5, ka 3.

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

Tātaihia te 1 mā te pū o 44, kia riro ko 1.

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

Tangohia te 1 i te 9+2i, ka 8+2i.

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

Whakareatia te taurunga me te tauraro ki te haumi hiato o te tauraro, 8-2i.

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

Mahia ngā whakarea i roto o \frac{3\left(8-2i\right)}{\left(8+2i\right)\left(8-2i\right)}.

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

Whakawehea te 24-6i ki te 68, kia riro ko \frac{6}{17}-\frac{3}{34}i.

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

Wāhi Tūturu

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

Ngā Upane Otinga

Hei whakarea i ngā pū o te pūtake kotahi, me tāpiri ō rātou taupū. Tāpiria te 35 me te 9 kia riro ai te 44.

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

Tātaihia te 1 mā te pū o 80, kia riro ko 1.

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

Tātaihia te i mā te pū o 12, kia riro ko 1.

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

Tāpirihia te 1 ki te 1, ka 2.

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

Tātaihia te i mā te pū o 26, kia riro ko -1.

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

Whakareatia te 3 ki te -1, ka -3.

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

Ko te tauaro o -3 ko 3.

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

Tāpirihia te 2 ki te 3, ka 5.

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

Tātaihia te i mā te pū o 14, kia riro ko -1.

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

Whakareatia te 2 ki te -1, ka -2.

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

Tangohia te 2 i te 5, ka 3.

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

Tātaihia te 1 mā te pū o 44, kia riro ko 1.

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

Tangohia te 1 i te 9+2i, ka 8+2i.

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

Me whakarea te taurunga me te tauraro o \frac{3}{8+2i} ki te haumi hiato o te tauraro, 8-2i.

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

Mahia ngā whakarea i roto o \frac{3\left(8-2i\right)}{\left(8+2i\right)\left(8-2i\right)}.

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

Whakawehea te 24-6i ki te 68, kia riro ko \frac{6}{17}-\frac{3}{34}i.

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

Ko te wāhi tūturu o \frac{6}{17}-\frac{3}{34}i ko \frac{6}{17}.

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