Question

If (x + yi) + 6i = 2, what is x + yi?

Answer 1

2-6i I think

Answer 2

See, in case of complex numbers, real part is equal to real part and imaginary part is equal to imaginary part..

Answer 3

\(x + iy + 6i = 2\)

Answer 4

The term without i is real and the term with i are imaginary..

Answer 5

Real on left side is \(x\) and real on right side is 2..

Answer 6

So, \(x=2\)..

Answer 7

On left side, imaginary part is : 6i + yi, and on right, there is no imaginary part, or you can say it is 0..

Answer 8

\(yi + 6i = 0 \\ (y+6)i = 0 \\ y = -6\)

Answer 9

Therefore, you know x and y values now..

\(x+iy = 2 + i(-6) \\ x + i y = 2 - 6i\)

Answer 10

Thank you @waterineyes

Answer 11

\(\dagger\)