Question

Write the expression in the standard form a plus b i.
left parenthesis 6 plus 7 i right parenthesis minus left parenthesis 7 minus 5 i right parenthesis

Answer 1

To simplify the expression \((6 + 7i) - (7 - 5i)\), we'll first distribute the negative sign across the terms inside the second parentheses:

\[
(6 + 7i) - (7 - 5i) = (6 + 7i) - 7 + 5i
\]

Now, we can combine like terms. Start with the real parts:

\[
6 - 7 = -1
\]

Next, combine the imaginary parts:

\[
7i + 5i = 12i
\]

Putting it all together, we have:

\[
-1 + 12i
\]

So, the expression in standard form \(a + bi\) is:

\[
-1 + 12i
\]