What is (t-ti+2i)^2(1-i) ?

The solution to (t-ti+2i)^2(1-i) is (-2t^2+8t-4)+(4-2t^2)i

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simplify (t-ti+2i)^2(1-i)

simplify

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

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

Solution steps

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

Apply the distributive law:

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

Simplify

(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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What is (t-ti+2i)^2(1-i) ?
The solution to (t-ti+2i)^2(1-i) is (-2t^2+8t-4)+(4-2t^2)i