Answer:
[tex]\frac{28-3i}{26}[/tex]
Step-by-step explanation:
For #2, remember that [tex]i=\sqrt{-1}[/tex], so [tex]i^{2}=-1[/tex] Also, (a+b)(a-b), where a and b are any numbers, (a+b)(a-b)=[tex]a^2-b^2[/tex]. 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 [tex]a+bi[/tex], where a and b are any numbers, the conjugate is always [tex]a-bi[/tex]. Lets apply these rules. The conjugate of 4+6i is 4-6i, so do this:
[tex]\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}[/tex]
Our answer is (28-3i)/(26)!
