SOLUTION: 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

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.
#1) 8i divided by 4-3i

#2) -15-^-18 divided by 33

#3) ^-75-^-300

Answer by CharlesG2(834) (Show Source): You can put this solution on YOUR website!
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

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