Whakaoti i te z=(a+5)i^6+(a-3)i^7

$$z = ( a + 5 ) i ^ { 6 } + ( a - 3 ) i ^ { 7 }$$

Whakaoti mō a

$$a=\left(-\frac{1}{2}+\frac{1}{2}i\right)z+\left(-1+4i\right)$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tātaihia te i mā te pū o 6, kia riro ko -1.

$$z=\left(a+5\right)\left(-1\right)+\left(a-3\right)i^{7}$$

Whakamahia te āhuatanga tohatoha hei whakarea te a+5 ki te -1.

$$z=-a-5+\left(a-3\right)i^{7}$$

Tātaihia te i mā te pū o 7, kia riro ko -i.

$$z=-a-5+\left(a-3\right)\left(-i\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te a-3 ki te -i.

$$z=-a-5-ia+3i$$

Pahekotia te -a me -ia, ka \left(-1-i\right)a.

$$z=\left(-1-i\right)a-5+3i$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$\left(-1-i\right)a-5+3i=z$$

Me tāpiri te 5 ki ngā taha e rua.

$$\left(-1-i\right)a+3i=z+5$$

Tangohia te 3i mai i ngā taha e rua.

$$\left(-1-i\right)a=z+5-3i$$

He hanga arowhānui tō te whārite.

$$\left(-1-i\right)a=z+\left(5-3i\right)$$

Whakawehea ngā taha e rua ki te -1-i.

$$\frac{\left(-1-i\right)a}{-1-i}=\frac{z+\left(5-3i\right)}{-1-i}$$

Mā te whakawehe ki te -1-i ka wetekia te whakareanga ki te -1-i.

$$a=\frac{z+\left(5-3i\right)}{-1-i}$$

Whakawehe z+\left(5-3i\right) ki te -1-i.

$$a=\left(-\frac{1}{2}+\frac{1}{2}i\right)z+\left(-1+4i\right)$$

Whakaoti mō z

$$z=\left(-1-i\right)a+\left(-5+3i\right)$$