What is (3(1-t)-it)^2 ?

The solution to (3(1-t)-it)^2 is ((3(1-t))^2-t^2)+(-6t+6t^2)i

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simplify (3(1-t)-it)^2

simplify

(3 (1 - t) - i t)^{2}

((3 (1 - t))^{2} - t^{2}) + (- 6 t + 6 t^{2}) i

Solution steps

(3 (1 - t) - i t)^{2}

Apply Perfect Square Formula:

(a - b)^{2} = a^{2} - 2 ab + b^{2}

(3 (1 - t) - i t)^{2} = (3 (1 - t))^{2} - 2 \cdot 3 (1 - t) i t + (i t)^{2}

= (3 (1 - t))^{2} - 2 \cdot 3 (1 - t) i t + (i t)^{2}

- 2 \cdot 3 (1 - t) i t = - 6 t i (1 - t)

(i t)^{2} = - t^{2}

= (3 (1 - t))^{2} - 6 t i (1 - t) - t^{2}

Expand

- 6 t i (1 - t) : - 6 t i + 6 t^{2} i

= (3 (1 - t))^{2} - 6 t i + 6 t^{2} i - t^{2}

Rewrite in standard complex form:

((3 (1 - t))^{2} - t^{2}) + (- 6 t + 6 t^{2}) i

= ((3 (1 - t))^{2} - t^{2}) + (- 6 t + 6 t^{2}) i

(a + b)^{2} - 2 a b

\frac{( x - 4 ) ( x + 6 )}{x}

2 (3 + 7)

r (t - sin (t))

\frac{31.3 x ^{2} + 47.3 x + 49}{x ^{2} ( x ^{2} + 50.3 )}

What is (3(1-t)-it)^2 ?
The solution to (3(1-t)-it)^2 is ((3(1-t))^2-t^2)+(-6t+6t^2)i