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Evaluate (6 + 2i) ÷ (3 – i). Option 1. Five fourths plus six fourths i Option 2 Eight fifths plus six fifths i Option 3 Twenty eighths plus twelve eighths iOption 4 Sixteen ninths plus twelve ninths i

Respuesta :

[tex]\frac{6+2i}{3-i}[/tex]

To simplify the expression above, multiply the numerator and denominator by the conjugate of 3 - i.

[tex]\frac{6+2i}{3-i}\times\frac{3+i}{3+i}[/tex][tex]\frac{6(3+i)+2i(3+i)}{3(3+i)-i(3+i)}\Rightarrow\frac{18+6i+6i-2}{9+3i-3i+1}\Rightarrow\frac{16+12i}{10}[/tex]

Then, separate the numerators.

[tex]\frac{16}{10}+\frac{12i}{10}[/tex]

Then, simplify each fraction.

[tex]\frac{8}{5}+\frac{6i}{5}[/tex]

Therefore, when evaluated, the given expression is equal to 8/5 + 6i/5. (Option 2)

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