Whakaoti i te i(1+4i)^3/(3-2i)^2

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

Aromātai

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

Ngā Upane Otinga

Tātaihia te 1+4i mā te pū o 3, kia riro ko -47-52i.

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

Whakareatia te i ki te -47-52i, ka 52-47i.

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

Tātaihia te 3-2i mā te pū o 2, kia riro ko 5-12i.

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

Whakareatia te taurunga me te tauraro ki te haumi hiato o te tauraro, 5+12i.

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

Mahia ngā whakarea i roto o \frac{\left(52-47i\right)\left(5+12i\right)}{\left(5-12i\right)\left(5+12i\right)}.

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

Whakawehea te 824+389i ki te 169, kia riro ko \frac{824}{169}+\frac{389}{169}i.

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

Wāhi Tūturu

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

Ngā Upane Otinga

Tātaihia te 1+4i mā te pū o 3, kia riro ko -47-52i.

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

Whakareatia te i ki te -47-52i, ka 52-47i.

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

Tātaihia te 3-2i mā te pū o 2, kia riro ko 5-12i.

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

Me whakarea te taurunga me te tauraro o \frac{52-47i}{5-12i} ki te haumi hiato o te tauraro, 5+12i.

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

Mahia ngā whakarea i roto o \frac{\left(52-47i\right)\left(5+12i\right)}{\left(5-12i\right)\left(5+12i\right)}.

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

Whakawehea te 824+389i ki te 169, kia riro ko \frac{824}{169}+\frac{389}{169}i.

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

Ko te wāhi tūturu o \frac{824}{169}+\frac{389}{169}i ko \frac{824}{169}.

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