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受欢迎的代数 >

化简 (x-13i)(x+5+10i)(x-5-10i)

解答

化简

(x - 13 i) (x + 5 + 10 i) (x - 5 - 10 i)

解答

(x^{3} + 75 x - 1300) + (- 13 x^{2} - 100 x - 975) i

求解步骤

(x - 13 i) (x + 5 + 10 i) (x - 5 - 10 i)

将

x + 5 + 10 i

改写成标准复数形式:

(x + 5) + 10 i

将

x - 5 - 10 i

改写成标准复数形式:

(x - 5) - 10 i

= (x - 13 i) ((x + 5) + 10 i) ((x - 5) - 10 i)

使用复数算数法则:

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

= ((x (x + 5) - (- 13) \cdot 10) + (x \cdot 10 - 13 (x + 5)) i) ((x - 5) - 10 i)

使用复数算数法则:

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

= ((x (x + 5) - (- 13) \cdot 10) (x - 5) - (x \cdot 10 - 13 (x + 5)) (- 10)) + ((x (x + 5) - (- 13) \cdot 10) (- 10) + (x \cdot 10 - 13 (x + 5)) (x - 5)) i

化简

((x (x + 5) - (- 13) \cdot 10) (x - 5) - (x \cdot 10 - 13 (x + 5)) (- 10)) + ((x (x + 5) - (- 13) \cdot 10) (- 10) + (x \cdot 10 - 13 (x + 5)) (x - 5)) i : (x^{3} + 75 x - 1300) + (- 13 x^{2} - 100 x - 975) i

= (x^{3} + 75 x - 1300) + (- 13 x^{2} - 100 x - 975) i

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