Question 318836
how do you simplify these problems? and what does the instructions mean when it says "leave your answers in the standard form of a complex number?" i only had 3 questions so i put them all on one page. i hope this was ok. 

on #2 and #3 I have no idea what you mean by the "^" symbol, so please repost those 2, I can show you how to do #1

#1) 8i divided by 4-3i

standard form of a complex number is a+bi, where a and b are real numbers, and i is an imaginary number, and i^2 = -1
the conjugate of a complex number is a-bi

8i/(4 - 3i) you will need to multiply top and bottom by the conjugate of 4 - 3i which is 4 + 3i

8i/(4 - 3i) * (4 + 3i)/(4 + 3i)
8i(4 + 3i)/((4 - 3i)(4 + 3i)) (use FOIL on the denominator)
(32i + 24i^2)/(16 + 12i - 12i - 9i^2)
(-24 + 32i)/(16 + 9)
(-24 + 32i)/25
-24/25 + (32/25)i
check:
(-24/25 + (32/25)i)(4 - 3i) (use FOIL)
(-24/25)(4) + (24/25)(3i) + (32/25)(4i) - (32/25)(3)(i^2)
(-96/25) + (72/25)i + (128/25)i + (96/25)
(72/25)i + (128/25)i = (200/25)i = 8i