simplify (z+20i)^2

Solution

simplify

(z + 20 i)^{2}

(z^{2} - 400) + 40 z i

Solution steps

(z + 20 i)^{2}

Apply Perfect Square Formula:

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

(z + 20 i)^{2} = z^{2} + 2 z \cdot 20 i + (20 i)^{2}

= z^{2} + 2 z \cdot 20 i + (20 i)^{2}

2 z \cdot 20 i = 40 z i

(20 i)^{2} = - 400

= z^{2} + 40 z i - 400

Rewrite in standard complex form:

(z^{2} - 400) + 40 z i

= (z^{2} - 400) + 40 z i

x + 5 \cdot (x + 5 - x - 5)

(x^{3} - (\frac{1}{x ^{2}}))^{5}

(z - \frac{1}{6}) (z + \frac{1}{6})

\frac{22}{( x - 1 ) ( x + 1 )}

\frac{1}{10} - \frac{1}{200} (0.98 - 1) - \frac{3}{50} (3.04 - 3)