化简 (t-ti+2i)^2(1-i)

解答

化简

(t - t i + 2 i)^{2} (1 - i)

(- 2 t^{2} + 8 t - 4) + (4 - 2 t^{2}) i

求解步骤

(t - t i + 2 i)^{2} (1 - i)

使用分配律:

a (b - c) = ab - a c

(t - t i + 2 i)^{2} (1 - i) = (t - t i + 2 i)^{2} \cdot 1 - (t - t i + 2 i)^{2} i

= (t - t i + 2 i)^{2} \cdot 1 - (t - t i + 2 i)^{2} i

化简

(t - t i + 2 i)^{2} \cdot 1 - (t - t i + 2 i)^{2} i : 4 i - 2 t^{2} i - 2 t^{2} + 8 t - 4

= 4 i - 2 t^{2} i - 2 t^{2} + 8 t - 4

Rewrite in standard complex form:

(- 2 t^{2} + 8 t - 4) + (4 - 2 t^{2}) i

= (- 2 t^{2} + 8 t - 4) + (4 - 2 t^{2}) i

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