Question

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

Answer 1

do you know what i stands for?

Answer 2

no

Answer 3

well… do you know roots and radicals?

Answer 4

Wait is it an imaginary number ?

Answer 5

yeahhhh, coocoobird! that is correct
so do you know what is an imaginary number?

Answer 6

Yes

Answer 7

so how come you're having trouble answering?

Answer 8

I just wanted someone else to explain it to me

Answer 9

http://www.mathsisfun.com/numbers/imaginary-numbers.html

Answer 10

when you fully grasp what an imaginary number is, then we will solve your problem.

Answer 11

Answering this question boils down to understanding when two complex numbers are equal. There is no algebra involved, only definitions.

Answer 12

Okay so it's not just imanginary numbers @mathteacher1729

Answer 13

Are you saying that x,y, and i are all variables? If I were to guess, it seems like the problem is asking when to complex (or imaginary) numbers are equal. If x,y, and i are all variables, then there is no way to solve exactly because you have one equation with three unknowns.

Answer 14

It's about complex numbers

Answer 15

@mathteacher1729

Answer 16

In that case you just match up the real component (the part not multiplied by i) and the imaginary component (the part being multiplied by i).



Two complex numbers \[a + bi \text{ and } c + di \] are equal when \[a = c \text{ and } b = d\]

Now look at \[-3 + yi \\
x + 6i\]

What does x need to be and what does y need to be?

Answer 17

x= -3
y= 6i ? @mathteacher1729

Answer 18

@lornbeach Yup, you got it! :)

Answer 19

But they just cancel eachother out ! @mathteacher1729

Answer 20

You're thinking of solving an equation.
You're not solving an equation here.

You're just finding out what values make two complex numbers equal to each other. There is no arithmetic or algebra or anything else going on in this problem.

Answer 21

Ohh thank you ((: