The given fraction in the simplest form is,[tex]-1.63+0.42i[/tex].
What is a fraction simplification?
Fraction simplification is a method of fraction reduction that entails making a fraction as simple as possible.
This is accomplished by dividing the numerator and denominator by the biggest integer that divides both integers exactly.
Given fraction:
[tex]\rm \rightarrow \frac{5+4i}{6+8i} \\\\ \rm \rightarrow \frac{5+4i}{6+8i} \frac{ \times 6-8i}{ \times 6-8i}\\\\ \frac{30+4i+24i-32i^2}{36-64} \\\\ \frac{30+4i+24i+32}{36-64} \\\\ -\frac{62-16i}{-38} \\\\ -1.63+0.42i[/tex]
Hence, the given fraction in the simplest form is,[tex]-1.63+0.42i[/tex].
To learn more about fraction simplification, refer to https://brainly.com/question/11479469.
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