Question

find real numbers a and b such that the equation is true
(a-1)+(b+3)i=5+8i

Answer 1

In equations like this you can always separate real and imaginary numbers into separate equations.

So, hypothetically if you had x+yi = 4 - 3i you could separate the equation to x=4 and yi= -3i, so x=4 and y= -3

Now back to your question:
First you multiply things out (this isn't that important for the above question, but could be if you had to keep track of multiplying i's together i.e. x + (y+zi)*(i+3) = 8. I won't solve it, but you would have to "FOIL" that last part.)
so... back to your question again.

multiplying stuff out...
a - 1 + b*i +3*i = 5 + 8*i
separate into separate equations for real and imaginary (as shown at top)
a - 1 = 5
b*i + 3*i = 8*i
now solve using basic algebra to get...
a = 6
b*i = 5*i, therefore b=5

Answer 2

No direct answers, please.

Answer 3

I hope I helped enough @Patsfan12 :)

Answer 4

thanks! your explanation was very thorough :)

Answer 5

no problem! ask me any questions u help with ;)

Answer 6

i will don't worry XD

Answer 7

lol

Answer 8

and please fan me

Answer 9

I thought I did?

Answer 10

yes I am :)

Answer 11

ok thanks :P

Answer 12

Ok @sidmanfu the instructions are to perform the operation and write the result in standard form:
sqrt(-6) x sqrt(-2)