### Instruction: If $z=3+4i$, find $z^2$. (Note that $i^2 = -1.$).### Response: To find $z^2$, I can use the formula $(a+bi)^2 = a^2 - b^2 + 2abi$, where $a$ and $b$ are the real and imaginary parts of $z$.
In this case, $a=3$ and $b=4$, so I can plug them into the formula.
I get $(3+4i)^2 = 3^2 - 4^2 + 2(3)(4)i$.
Simplifying, I get $9 - 16 + 24i$.