Question

Find the real numbers x and y that make the equation true.
-3 + yi = x + 6i

Answer 1

compare the real parts of both sides
and
compare the imaginary parts of both sides

a+bi
a is the real part
b is the imaginary part


so
what is the real part of -3+yi and the real part of x+6i?

Answer 2

-3 and x is the real part?

Answer 3

so x=-3

Answer 4

so now compare the coefficients of the imaginary unit of i of both sides
that is what is the imaginary part of -3+yi and x+6i?

Answer 5

yi and 6i

Answer 6

so what must y be
so that yi=6i

Answer 7

y = (6i)/i? can I simiplfy that?

Answer 8

simplify*

Answer 9

well looks like you are trying to solve for y even though there is really nothing to solve
but I suppose you can do this longer way
it isn't too much longer anyways
but yeah what is i/i ?

Answer 10

1, so the i's cancel out and I'm just left 6?

Answer 11

yep

but you could have skipped all of that
yi=6i
is only satisfied when y is 6

Answer 12

okay, thank you so much!!

Answer 13

no problem
in general
if you have
(Let x,y,a,b be real numbers)

x+yi=a+bi

then
x=a and y=b

Answer 14

So for future refernece I just have to separate the real and imaginary parts and solve for the variable, that makes sense, thanks!

Answer 15

yep yep

example:
3+yi=x-9i+2i

anyways first write this as
3+yi=x-7i

so x=3 and y=-7

Answer 16

thank you :)

Answer 17

np :)