simplify (3z-4i)^2

Solution

simplify

(3 z - 4 i)^{2}

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

Solution steps

(3 z - 4 i)^{2}

Apply Perfect Square Formula:

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

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

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

(3 z)^{2} = 9 z^{2}

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

(4 i)^{2} = - 16

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

Rewrite in standard complex form:

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

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

\frac{2 x ^{3} - 4 x ^{2} - 15 x + 8}{( x - 1 ) ^{2}}

(\frac{( x ^{2} - 4 )}{x} - k)^{2}

\frac{4 - s}{( s + 2 j ) ( s - 2 j ) ( s + 1 )}

\frac{\frac{d}{d x} ( 2 x ^{2} ) - 13 x + 22}{( x - 2 ) ^{2}}

d (1 + x e^{y})