Let $z = (8+7i)$ and $w = (8-7i)$. Compute the following (enter in the form $a + bi$ where $a$ and $b$ are real numbers):

(a) $z + w =$ $+$ $i$

(b) $z - w =$ $+$ $i$

(c) $zw =$ $+$ $i$

(d) $\dfrac{z}{w} =$ $+$ $i$

Hint: