To solve the problem of writing [tex]\(\sqrt{64} - \sqrt{-289}\)[/tex] as a complex number in the form of [tex]\(a + bi\)[/tex], follow these steps:
1. Calculate the square root of 64:
[tex]\[
\sqrt{64} = 8
\][/tex]
since [tex]\(8 \times 8 = 64\)[/tex].
2. Calculate the square root of -289:
The square root of a negative number introduces the imaginary unit [tex]\(i\)[/tex], where [tex]\(i = \sqrt{-1}\)[/tex]. So,
[tex]\[
\sqrt{-289} = \sqrt{289} \cdot i = 17i
\][/tex]
because [tex]\(17 \times 17 = 289\)[/tex].
3. Combine the results:
Now, substitute the calculated values into the original expression [tex]\(\sqrt{64} - \sqrt{-289}\)[/tex]:
[tex]\[
\sqrt{64} - \sqrt{-289} = 8 - 17i
\][/tex]
4. Express the result as a complex number:
The expression [tex]\(8 - 17i\)[/tex] is already in the form [tex]\(a + bi\)[/tex], where [tex]\(a = 8\)[/tex] and [tex]\(b = -17\)[/tex].
Thus, the expression [tex]\(\sqrt{64} - \sqrt{-289}\)[/tex] as a complex number in the form [tex]\(a + bi\)[/tex] is [tex]\(8 - 17i\)[/tex].
The correct answer is:
A. [tex]\(8 - 17i\)[/tex].
