化简 (x-2)^2(x-3i)^2

解答

化简

(x - 2)^{2} (x - 3 i)^{2}

(x^{4} - 4 x^{3} - 5 x^{2} + 36 x - 36) + (- 6 x^{3} + 24 x^{2} - 24 x) i

求解步骤

(x - 2)^{2} (x - 3 i)^{2}

展开

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

= (x^{2} - 4 x + 4) (x - 3 i)^{2}

= (x - 3 i)^{2} (x^{2} - 4 x + 4)

展开

(x - 3 i)^{2} : x^{2} - 6 x i - 9

= (x^{2} - 6 x i - 9) (x^{2} - 4 x + 4)

打开括号

= x^{2} x^{2} + x^{2} (- 4 x) + x^{2} \cdot 4 - 6 x i x^{2} - 6 x i (- 4 x) - 6 x i 4 - 9 x^{2} - 9 (- 4 x) - 9 \cdot 4

化简

x^{2} x^{2} + x^{2} (- 4 x) + x^{2} \cdot 4 - 6 x i x^{2} - 6 x i (- 4 x) - 6 x i 4 - 9 x^{2} - 9 (- 4 x) - 9 \cdot 4 : x^{4} - 4 x^{3} - 5 x^{2} - 6 x^{3} i + 24 x^{2} i - 24 x i + 36 x - 36

= x^{4} - 4 x^{3} - 5 x^{2} - 6 x^{3} i + 24 x^{2} i - 24 x i + 36 x - 36

Rewrite in standard complex form:

(x^{4} - 4 x^{3} - 5 x^{2} + 36 x - 36) + (- 6 x^{3} + 24 x^{2} - 24 x) i

= (x^{4} - 4 x^{3} - 5 x^{2} + 36 x - 36) + (- 6 x^{3} + 24 x^{2} - 24 x) i

e x p an d \frac{lo g _{10} ( 2 )}{lo g _{10} ( 5 b )}

e x p an d 4 (x^{2} + y^{2}) (2 x + 2 y \frac{d y}{d x})

e x p an d \frac{1}{( s - 2 ) ( s + 1 )}

e x p an d \frac{2 X + 1}{( X - 1 ) ( 2 X ^{3} + 6 X ^{2} - X + 4 )}

s im pl i f y e^{- i \cdot x} \cdot (6 + e^{i \cdot x} + e^{- i \cdot x})