化简 (1+it)^2

解答

化简

(1 + i t)^{2}

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

求解步骤

(1 + i t)^{2}

使用完全平方公式:

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

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

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

1^{2} = 1

2 \cdot 1 i t = 2 t i

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

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

Rewrite in standard complex form:

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

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

e x p an d e^{3 x} \cdot (3 x^{2} y + 2 x y + y^{3})

e x p an d e^{2} t (sin (2 t) - 1)

e x p an d sinh ((x - b) (x - c)) (2 x - c - b)

s im pl i f y (x + 1) \cdot (x + 2)

s im pl i f y x (x^{2} - 2 x + \frac{1}{2})