Question

Which expression is equivalent to (4+6i)
2
?
A. −20+48i B. 8+12i C. 16−36i D. 20+48i

Answer 1

To find the expression equivalent to \((4 + 6i)^2\), we can expand it using the formula for the square of a binomial \((a + b)^2 = a^2 + 2ab + b^2\).

Here, \(a = 4\) and \(b = 6i\).

\[
(4 + 6i)^2 = 4^2 + 2(4)(6i) + (6i)^2
\]

Calculating each term:

1. \(4^2 = 16\)
2. \(2(4)(6i) = 48i\)
3. \((6i)^2 = 36i^2\). Since \(i^2 = -1\), it becomes \(36(-1) = -36\).

Now, putting it all together:

\[
(4 + 6i)^2 = 16 + 48i - 36
\]

Combine like terms:

\[
16 - 36 + 48i = -20 + 48i
\]

Thus, the expression equivalent to \((4 + 6i)^2\) is \(-20 + 48i\).

The correct answer is **A. −20 + 48i**.