Question

PLEASE HELP!! Algebra 2 Review !!

Answer 1

Answer:

$\frac{28-3i}{26}$

Step-by-step explanation:

For #2, remember that $i=\sqrt{-1}$, so $i^{2}=-1$ Also, (a+b)(a-b), where a and b are any numbers, (a+b)(a-b)=$a^2-b^2$. Now, to simplify, or radicalize, a number with surds in the denominator, you have to multiply the denominator by its conjugate. If there is a complex number $a+bi$, where a and b are any numbers, the conjugate is always $a-bi$. Lets apply these rules. The conjugate of 4+6i is 4-6i, so do this:

$\frac{5+6i}{4+6i}=\frac{(5+6i)(4-6i)}{(4+6i)(4-6i)}=\frac{20+24i-30i+36}{16+36}=\frac{56-6i}{52}=\frac{2(28-3i)}{2(26)}=\frac{28-3i}{26}$

Our answer is (28-3i)/(26)!