Question

Multiply.
​(5plus6i​)squared
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Part 1
​(5plus6i​)squaredequals
  
enter your response here
​(Type your answer in the form a​ + bi​.)

Answer 1

To square the complex number \( (5 + 6i) \), we can use the formula for squaring a binomial:

\[
(a + b)^2 = a^2 + 2ab + b^2
\]

Here, let \( a = 5 \) and \( b = 6i \).

Now we can compute each part:

1. \( a^2 = 5^2 = 25 \)
2. \( 2ab = 2 \cdot 5 \cdot 6i = 60i \)
3. \( b^2 = (6i)^2 = 36i^2 = 36(-1) = -36 \)

Now, put it all together:

\[
(5 + 6i)^2 = a^2 + 2ab + b^2 = 25 + 60i - 36
\]

Combining the real parts:

\[
25 - 36 = -11
\]

Thus, we have:

\[
(5 + 6i)^2 = -11 + 60i
\]

So, the final answer is:

\[
\boxed{-11 + 60i}
\]