To simplify the complex fraction [tex]\(\frac{2-18i}{9}\)[/tex], let's break it down step by step.
1. Rewrite the fraction:
[tex]\[
\frac{2-18i}{9} = \frac{2}{9} - \frac{18i}{9}
\][/tex]
We can split the numerator into two separate parts over the common denominator.
2. Simplify each part:
[tex]\[
\frac{2}{9} \quad \text{and} \quad \frac{18i}{9}
\][/tex]
We can simplify each fraction separately.
3. Simplify [tex]\(\frac{2}{9}\)[/tex]:
[tex]\[
\frac{2}{9}
\][/tex]
This fraction is already in its simplest form.
4. Simplify [tex]\(\frac{18i}{9}\)[/tex]:
[tex]\[
\frac{18i}{9} = 2i
\][/tex]
We divide 18 by 9 to get 2.
5. Combine the simplified parts:
[tex]\[
\frac{2}{9} - 2i
\][/tex]
Thus, the simplified form of the fraction [tex]\(\frac{2-18i}{9}\)[/tex] is:
[tex]\[
\frac{2}{9} - 2i
\][/tex]
In numerical representations:
[tex]\[
0.2222222222222222 - 2i
\][/tex]
So, the step-by-step simplified form is [tex]\(\frac{2}{9} - 2i\)[/tex].
