Question

multiply.
$(6 + 8i)^2$
$(6 + 8i)^2 = \square$
(type your answer in the form $a + bi$.)

Explanation:

Step1: Expand using square formula

Recall that $(a+b)^2 = a^2 + 2ab + b^2$. For $(6+8i)^2$:
$$(6+8i)^2 = 6^2 + 2(6)(8i) + (8i)^2$$

Step2: Calculate each term

Compute each part separately:
$6^2 = 36$, $2(6)(8i) = 96i$, $(8i)^2 = 64i^2$. Since $i^2 = -1$, $64i^2 = 64(-1) = -64$.

Step3: Combine real and imaginary terms

Add the real parts and imaginary parts together:
$$36 + 96i - 64 = (36-64) + 96i$$

Answer:

$-28 + 96i$