SOLUTION: I wanted you to check my answers on these two problems: 1) Problem: (2-4i)(2-i) 4-2i-4i-4i^2 4-6i-4i^2 4-6i-4i^2(-1) 4-6i+4 answer: 8-6i 2) Problem: 3

Question 163638: I wanted you to check my answers on these two problems:
1) Problem: (2-4i)(2-i)
4-2i-4i-4i^2
4-6i-4i^2
4-6i-4i^2(-1)
4-6i+4
answer: 8-6i
2) Problem: 3+5i/1+i
3+5i/1+i . i/i
3i+5i^2/i+i^2
3i+5(-1)/i+i(-1) = -3i-5/-1-1 =
answer: -3i-5/-2i
Thanks.

Found 2 solutions by checkley77, gonzo:
Answer by checkley77(12844) (Show Source): You can put this solution on YOUR website!
(2-4i)(2-i)
4-2i-[8i][+4i^2]
4-10i+4i^2
4-10i+4*-1
4-10i-4
-10i Answer.
-----------------------
3+(5i/1)+i
3+5i+i
3+6i
3(1+2i) Answer.
OR 3+5i/(1+i)
[3(1+i)+5i]/(1+i)
[3+3i+5i]/(1+i)
[3+8i)/(1+i)

Answer by gonzo(654) (Show Source): You can put this solution on YOUR website!
i don't get the answers you do.
here's what i did.
-----
problem 1:
-----
(2-4i)*(2-i)
using FOIL
First..(F) = 2*2 = 4
Outer..(O) = 2*-i = -2i
Inner..(I) = -4i*2 = -8i
Last...(L) = -4i*-i = +4i^2
adding like terms together gets
4 - 10i + 4i^2
i^2 = -1 so 4i^2 becomes -4
equation then becomes
4 - 10i - 4
which becomes -10i
answer looks like it should be -10i
-----
problem 2:
-----
(3+5i)/(1+i)
multiply numerator and denominator by (1-i) and equation becomes
((3+5i)*(1-i))/((1+i)*(1-i))
-----
using FOIL to multiply numerator gets
numerator = (3+5i)*(1-i)
First = 3*1 = 3
Outer = 3*-i = -3i
Inner = 5i*1 = +5i
Last = 5i*-i = -5i^2
combining like terms and numerator becomes
3 + 2i - 5i^2
since i^2 = -1, numerator becomes
3 + 2i - 5*(-1)
which becomes
3 + 2i + 5
which becomes
8 + 2i
numerator = 8+2i
-----
using FOIL to multiply denominator gets
denominator = (1-i)*(1+i)
First = 1*1 = 1
Outer = 1*i = i
Inner = -i*1 = -i
Last = -i*i = -i^2
combining like terms and denominator becomes
1-i^2
since i^2 = -1 denominator becomes
1-(-1)
which becomes
1+1
which becomes
2
denominator = 2
-----
putting numerator and denominator back into the total equation and it becomes
(8+2i)/2
which becomes 4+i
answer looks like it should be 4+i
-----

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