Whakaoti i te 5(i+3)/(1+2i)(1-2i)*(2i)^4/(1+i)^3

$$\frac { 5 ( i + 3 ) } { ( 1 + 2 i ) ( 1 - 2 i ) } \cdot \frac { ( 2 i ) ^ { 4 } } { ( 1 + i ) ^ { 3 } }$$

Aromātai

$$-8-16i$$

Ngā Upane Otinga

Whakareatia te 1+2i ki te 1-2i, ka 5.

$$\frac{5\left(i+3\right)}{5}\times \frac{\left(2i\right)^{4}}{\left(1+i\right)^{3}}$$

Me whakakore te 5 me te 5.

$$\left(i+3\right)\times \frac{\left(2i\right)^{4}}{\left(1+i\right)^{3}}$$

Tātaihia te 2i mā te pū o 4, kia riro ko 16.

$$\left(i+3\right)\times \frac{16}{\left(1+i\right)^{3}}$$

Tātaihia te 1+i mā te pū o 3, kia riro ko -2+2i.

$$\left(i+3\right)\times \frac{16}{-2+2i}$$

Me whakarea te taurunga me te tauraro o \frac{16}{-2+2i} ki te haumi hiato o te tauraro, -2-2i.

$$\left(i+3\right)\times \frac{16\left(-2-2i\right)}{\left(-2+2i\right)\left(-2-2i\right)}$$

Mahia ngā whakarea i roto o \frac{16\left(-2-2i\right)}{\left(-2+2i\right)\left(-2-2i\right)}.

$$\left(i+3\right)\times \frac{-32-32i}{8}$$

Whakawehea te -32-32i ki te 8, kia riro ko -4-4i.

$$\left(i+3\right)\left(-4-4i\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te i+3 ki te -4-4i.

$$4-4i+\left(-12-12i\right)$$

Tāpirihia te 4-4i ki te -12-12i, ka -8-16i.

$$-8-16i$$

Wāhi Tūturu

$$-8$$

Ngā Upane Otinga

Whakareatia te 1+2i ki te 1-2i, ka 5.

$$Re(\frac{5\left(i+3\right)}{5}\times \frac{\left(2i\right)^{4}}{\left(1+i\right)^{3}})$$

Me whakakore te 5 me te 5.

$$Re(\left(i+3\right)\times \frac{\left(2i\right)^{4}}{\left(1+i\right)^{3}})$$

Tātaihia te 2i mā te pū o 4, kia riro ko 16.

$$Re(\left(i+3\right)\times \frac{16}{\left(1+i\right)^{3}})$$

Tātaihia te 1+i mā te pū o 3, kia riro ko -2+2i.

$$Re(\left(i+3\right)\times \frac{16}{-2+2i})$$

Me whakarea te taurunga me te tauraro o \frac{16}{-2+2i} ki te haumi hiato o te tauraro, -2-2i.

$$Re(\left(i+3\right)\times \frac{16\left(-2-2i\right)}{\left(-2+2i\right)\left(-2-2i\right)})$$

Mahia ngā whakarea i roto o \frac{16\left(-2-2i\right)}{\left(-2+2i\right)\left(-2-2i\right)}.

$$Re(\left(i+3\right)\times \frac{-32-32i}{8})$$

Whakawehea te -32-32i ki te 8, kia riro ko -4-4i.

$$Re(\left(i+3\right)\left(-4-4i\right))$$

Whakamahia te āhuatanga tohatoha hei whakarea te i+3 ki te -4-4i.

$$Re(4-4i+\left(-12-12i\right))$$

Tāpirihia te 4-4i ki te -12-12i, ka -8-16i.

$$Re(-8-16i)$$

Ko te wāhi tūturu o -8-16i ko -8.

$$-8$$