Answer:
[tex]-\frac{4}{7} -\frac{8}{7} i\sqrt{5}[/tex]
Step-by-step explanation:
To rationalize the denominator, we would have to multiply by the complex conjugate of 6 + 2i√5 which is 6 - 2i√5:
[tex]\frac{8-8i\sqrt{5} }{6+2i\sqrt{5} } *\frac{6-2i\sqrt{5} }{6-2i\sqrt{5} }[/tex]
The denominator resembles the difference of squares:
6^2 - (2i√5)^2
36 + 20
56
Next we would need to multiply the numerator, but before, notice we can factor out 8 from 8 - 8i√5:
[tex]\frac{8(1-i\sqrt{5})(6-2i\sqrt{5}) }{56}[/tex]
We can cancel that 8 with that 56 in the denominator:
[tex]\frac{6-2i\sqrt{5}-6i\sqrt{5}-10}{7}[/tex]
This simplifies to:
[tex]\frac{-4-8i\sqrt{5} }{7}[/tex]
which is the same as:
[tex]-\frac{4}{7} -\frac{8}{7} i\sqrt{5}[/tex]
