Question

solve for the real numbers X and Y

1.) 5i=x-yi
2.) x-3yi=8

Answer 1

more to come ill back later for clarifications

Answer 2

1) => y = -5 (if it should be real) but than 2) is not solve able in 2) y must be something like 0

Answer 3

Last time I checked zero was still a real number.

Answer 4

but the answers does not match
1) x := 0 , y := -5
2) x := 8 , y := 0

the x and the y are not the same !

Answer 5

We'll have to wait for moongazer to return to clarify if this is a system of equations or not.

Answer 6

Get everything over to the same side of the equation:
0 = x + 5 - y)i = 0 + 0i.
An important property of complex numbers is that two of them are equal if and only if their real components arr equal, and their complex components are equal. With that in mind, we have the following:
(i) x = 0, and
(ii) 5 - y = 0, implying y = 5.

Answer 7

I'm back!
so, how do we start?

Answer 8

Start by getting everything over to the same side of the equation.

Answer 9

=x-yi=5i
like that?

Answer 10

Have 0 be on one side. Everything else on the other.

Answer 11

0=x-yi-5i?
why should there be a zero if i am correct?

Answer 12

Now group all terms together that have an i in them.

Answer 13

why should there be a zero?
0=x-(y-5)i ?

Answer 14

An important thing to remember about complex numbers is that two of them are defined to be equal if and only if their real parts are equal, and their imaginary parts are equal.

Answer 15

The number 0 can be written as 0 + 0i.

Answer 16

A post appeared about twenty minutes that outlines the procedure that determines x = 0 and y = 5.

Answer 17

...twenty minutes ago...

Answer 18

sorry for the late reply

Answer 19

what happened to i?

Answer 20

Did you group the terms that have an i in them?

Answer 21

You might have x + (5 - y)i = 0 + 0i.

Answer 22

The real part of the left side of the equation is x, and its imaginary part is
5 - y,

Answer 23

The right-hand side of the equation has 0 as both its real and imaginary parts.

Answer 24

All that's left to do is set the corresponding parts equal.

Answer 25

what is the meaning of if and only if?

Answer 26

You'll have x = 0, and 5 - y = 0, implying y = 5.

Answer 27

If and only if mrans that the implication goes both ways. "A if and only if B" means that A implies B, and B implies A.

Answer 28

so the steps are ; put the equation on one side like =x-(y-5)i, and equate it to 0+0i ?
so it will become 0+0i = x-(y-5)i
then divide all sides by i
so it will become 0= x-y-5
is this correct?

Answer 29

You got the gist of it. Concerning the real and imaginary parts of a complex number:
they are real numbers, denoted bt Re(z) anf Im(z), where z is a complex number.

Answer 30

... by Re(z) and Im(z)...

Answer 31

please explain it in an easy manner i don't know what " denoted bt Re(z) anf Im(z), where z is a complex number" means

Answer 32

so, if my explanation is correct how did you get x and y?
sorry if i can't understand it easily.

Answer 33

could you make a conclusion that can easily be understand?

Answer 34

How do you tell if two complex numbers are equal?

Answer 35

if the imaginary and the real numbers have the same value

Answer 36

Right. So if I say that 2 + 3i = 2 - 5i, am I right?

Answer 37

no

Answer 38

You get the golden goode award :^)

Answer 39

...goose award.

Answer 40

?

Answer 41

Just goofing. You are right.

Answer 42

then what now? ^_^

Answer 43

Do you see why x = 0?

Answer 44

no
i am stuck with x-y-5

Answer 45

=0

Answer 46

You should have x + (5 - y)i = 0 + 0i.

Answer 47

then?

Answer 48

The i is still there. It doesn't vanish.

Answer 49

so, how do you equate it?

Answer 50

If the complex number on the left is the same as 0 + 0i, then x = 0, and 5 - y = 0.

Answer 51

Solve that last equation for y.