化简 (z^2+2z-7i)^2

解答

化简

(z^{2} + 2 z - 7 i)^{2}

(z^{4} + 4 z^{3} + 4 z^{2} - 49) + (- 14 z^{2} - 28 z) i

求解步骤

(z^{2} + 2 z - 7 i)^{2}

使用指数法则:

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

(z^{2} + 2 z - 7 i)^{2} = (z^{2} + 2 z - 7 i) (z^{2} + 2 z - 7 i)

= (z^{2} + 2 z - 7 i) (z^{2} + 2 z - 7 i)

打开括号

= z^{2} z^{2} + z^{2} \cdot 2 z + z^{2} (- 7 i) + 2 z z^{2} + 2 z \cdot 2 z + 2 z (- 7 i) - 7 i z^{2} - 7 i 2 z - 7 i (- 7 i)

化简

z^{2} z^{2} + z^{2} \cdot 2 z + z^{2} (- 7 i) + 2 z z^{2} + 2 z \cdot 2 z + 2 z (- 7 i) - 7 i z^{2} - 7 i 2 z - 7 i (- 7 i) : z^{4} + 4 z^{3} - 14 z^{2} i + 4 z^{2} - 28 z i - 49

= z^{4} + 4 z^{3} - 14 z^{2} i + 4 z^{2} - 28 z i - 49

Rewrite in standard complex form:

(z^{4} + 4 z^{3} + 4 z^{2} - 49) + (- 14 z^{2} - 28 z) i

= (z^{4} + 4 z^{3} + 4 z^{2} - 49) + (- 14 z^{2} - 28 z) i

e x p an d \frac{6 x ^{2} - 43 x + 50}{x ( x - 2 ) ( x - 5 )}

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

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

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

e x p an d \frac{x + 0.693}{( x - 0.385 ) ^{2}}