化简 (4z-3i)^2

解答

化简

(4 z - 3 i)^{2}

(16 z^{2} - 9) - 24 z i

求解步骤

(4 z - 3 i)^{2}

使用完全平方公式:

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

(4 z - 3 i)^{2} = (4 z)^{2} - 2 \cdot 4 z \cdot 3 i + (3 i)^{2}

= (4 z)^{2} - 2 \cdot 4 z \cdot 3 i + (3 i)^{2}

(4 z)^{2} = 16 z^{2}

- 2 \cdot 4 z \cdot 3 i = - 24 z i

(3 i)^{2} = - 9

= 16 z^{2} - 24 z i - 9

Rewrite in standard complex form:

(16 z^{2} - 9) - 24 z i

= (16 z^{2} - 9) - 24 z i

e x p an d (e^{x} - 1) (e^{x} + 1)

s im pl i f y (x - 4 i)^{2}

e x p an d \frac{5}{s ( s ^{2} + s + 2 )}

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

e x p an d \frac{6}{( s - 2 ) ^{4}}