How can I find x, y values for ( 1 + i ) x &#x221

sweetymoeyz 2022-07-06 Answered
How can I find x, y values for ( 1 + i ) x 2 i 3 + i + ( 2 3 i ) y + i 3 i = i
I believe the format I need in order to solve this problem should be such that the real parts and imaginary parts are separated, { R e a l } + { I m a g i n a r y } i = i
Then I can equate the real and imaginary parts of the equation and solve for x and y. I tried to multiply by the conjugate so that I would get a real number at the denominator.
Rearranged:
x + i ( x 2 ) 3 + i + 2 y + i ( 3 y + 1 ) 3 i = i
Multiplied by conjugate:
x ( 3 i ) + i ( x 2 ) ( 3 i ) 10 + 2 y ( 3 + i ) + i ( 3 y + 1 ) ( 3 + i ) 10 = i
And at this step I started to feel as if I made a mistake because I weren't sure how to proceed. Would someone let me know if my approach was correct and show me how to do this?
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Answers (1)

toriannucz
Answered 2022-07-07 Author has 16 answers
x ( 3 i ) + i ( x 2 ) ( 3 i ) 10 + 2 y ( 3 + i ) + i ( 3 y + 1 ) ( 3 + i ) 10 = i
3 x i x + 3 i x + x 6 i 2 + 6 y + 2 i y 9 i y + 3 y + 3 i 1 10 = i
4 x + 9 y 3 10 + i ( 2 x 7 y 3 ) 10 = 0 + i
4 x + 9 y 3 10 = 0   a n d   ( 2 x 7 y 3 ) 10 = 1
solve simultaneously to obtain values for x and y

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