Answer:
option B
[tex]\frac{31}{50}-\frac{4}{25} i[/tex]
Step-by-step explanation:
Given in the question a complex fraction
Step1
To divide complex numbers, you must multiply by the conjugate. To find the conjugate of a complex number all you have to do is change the sign between the two terms in the denominator.
[tex]\frac{5+4i}{6+8i}(\frac{6-8i}{6-8i})[/tex]
Step2
Distribute (or FOIL) in both the numerator and denominator to remove the parenthesis.
[tex]\frac{30+24i-40i-32i²}{36-64i^{2} }[/tex]
Step3
Simplify the powers of i, specifically remember that i² = –1.
[tex]\frac{62-16i}{36+64}[/tex]
Step4
[tex]\frac{62}{100}-\frac{16i}{100}[/tex]
Step5
simply
[tex]\frac{31}{50}-\frac{4}{25}i[/tex]
