simplify (1-t+ti)^2

Solution

simplify

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

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

Solution steps

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

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

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

= (1 - t + t i) (1 - t + t i)

Distribute parentheses

= 1 \cdot 1 + 1 \cdot (- t) + 1 \cdot t i - t \cdot 1 - t (- t) - tt i + t i 1 + t i (- t) + t i t i

Simplify

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

= - 2 t + 2 t i - 2 t^{2} i + 1

Rewrite in standard complex form:

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

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

(T - a) (T - c) (T - d) (T - e) (T - f)

r (2 - sin (θ))

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(z - 1.2) (z - 0.5) (z + 0.4)