Modulus and Square of a Complex Number

Consider the complex number $z = 3 + 4i$. Calculate the modulus of $z$ and then find the value of $z^2$.

The modulus of a complex number $a + bi$ is given by the formula $|z| = \sqrt{a^2 + b^2}$. To find $z^2$, you can expand the expression by multiplying $z$ by itself: $z^2 = (a + bi)(a + bi) = a^2 + 2abi + (bi)^2$.