Question

Simplify the expression $\frac{z^{570}-z^{480}}{2z^{30}}$

• A. $\frac{z^{540}-z^{450}}{2}$
• B. $\frac{z^{60}}{2}$
• C. $z^{30}$
• D. $\frac{z^{19}-z^{16}}{2}$

Answer 1

The correct option is A $\frac{z^{540}-z^{450}}{2}$

Given, $\frac{z^{570}-z^{480}}{2z^{30}}$

$=\frac{z^{570}}{2z^{30}}-\frac{z^{480}}{2z^{30}}$
$=\frac{z^{570}}{2z^{30}}-\frac{z^{480}}{2z^{30}}=\frac{z^{570-30}}{2}-\frac{z^{480-30}}{2}$
$=\frac{z^{540}}{2}-\frac{z^{450}}{2}=\frac{z^{540}-z^{450}}{2}$