5+y+(3x-7)i=9-3i

Question

find x and y in the equation make it true

 

Answer 1

Recall that if a+bi=c+di then a=c and b=d. In this case we have:

5+y=9 so y=9-5=4 and

3x-7=-3 so 3x=-3+7=4 so x=4/3

 

Answer 2

Alright so we are looking for what 'x=' and 'y=', so if we get them alone on one side of the equal sign it will tell us.
We can start singling out either variable but I happen to have chosen 'y' because it looks easier.

Subtract 5 from each side to make our equation: 'y+(3x-7)i=9-3i-5'

At this point I would distribute the 'i' via the distributive property and then move those two terms to the other side, making: 'y=9-3i-5-3xi+7i'

After some simple computation you can reduce to get '[]xi+[]i' and factor the 'i' out to get your 'y='.

When you have 'y=', plug that back in the place of 'y' and solve it out for 'x'. Example; '5+[]+(3x-7)i=9-3i'.
Then you should get both a 'x' and 'y' value, remember to check your work by plugging them back in.