simplify (1-i+t)^2

Solution

simplify

(1 - i + t)^{2}

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

Solution steps

(1 - i + t)^{2}

Apply exponent rule:

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

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

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

Distribute parentheses

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

Simplify

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

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

Rewrite in standard complex form:

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

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

(2 + 5) (1 + 2)

(x^{2} + 4) (x^{2} - 12 x + 4)

(x^{2} + 22 \cdot x + 4) \cdot (x^{2} - 22 \cdot x + 4)

(- 1 - 3) + i (1 - 3)

(1 - \frac{1}{( x + 3 )}) (1 - \frac{1}{x + 2}) (1 - \frac{1}{x + 1})