simplify (z-2i)^2

Solution

simplify

(z - 2 i)^{2}

(z^{2} - 4) - 4 z i

Solution steps

(z - 2 i)^{2}

Apply Perfect Square Formula:

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

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

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

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

(2 i)^{2} = - 4

= z^{2} - 4 z i - 4

Rewrite in standard complex form:

(z^{2} - 4) - 4 z i

= (z^{2} - 4) - 4 z i

\frac{2 ( x + h ) + 1 - 2 x + 1}{h}

(a + b + c + d + e)^{2}

\frac{1}{( x + 1 ) ( x + 2 )}

(3 x - 3) (3 x + 3)

(1 - x) (1 + x)