Question

multiply.
$(4 + 9i)^2$
$(4 + 9i)^2 = \square$
(type your answer in the form $a + bi$.)

Explanation:

Step1: Expand using square formula

$(a+b)^2 = a^2 + 2ab + b^2$, so:
$(4+9i)^2 = 4^2 + 2(4)(9i) + (9i)^2$

Step2: Calculate each term

$4^2=16$, $2(4)(9i)=72i$, $(9i)^2=81i^2$

Step3: Substitute $i^2=-1$

$81i^2 = 81(-1) = -81$

Step4: Combine real terms

$16 - 81 + 72i = -65 + 72i$

Answer:

$-65 + 72i$