化简 (2i)(1-4i)(1+i)

解答

化简

(2 i) (1 - 4 i) (1 + i)

6 + 10 i

求解步骤

(2 i) (1 - 4 i) (1 + i)

使用复数算数法则:

(a + bi) (c + d i) = (a c - b d) + (a d + b c) i

= 2 i ((1 \cdot 1 - (- 4) \cdot 1) + (1 \cdot 1 - 4 \cdot 1) i)

化简

(1 \cdot 1 - (- 4) \cdot 1) + (1 \cdot 1 - 4 \cdot 1) i : 5 - 3 i

= 2 i (5 - 3 i)

使用分配律:

a (b - c) = ab - a c

2 i (5 - 3 i) = 2 i 5 - 2 i 3 i

= 2 i 5 - 2 i 3 i

2 i 5 = 10 i

- 2 i 3 i = 6

= 10 i + 6

Rewrite in standard complex form:

6 + 10 i

= 6 + 10 i

s im pl i f y \frac{x - 1}{x - 1}

s im pl i f y 3 \frac{216}{16}

s im pl i f y \frac{36}{120}

s im pl i f y \frac{6}{26}

s im pl i f y \frac{11}{12} - \frac{5}{6}