Find x and y, if (6+i)(x+yi)=2 and, i^2=-1

boitshupoO

boitshupoO

Answered question

2021-08-20

Find x and y, if
(6+i)(x+yi)=2
and,
i2=1

Answer & Explanation

sweererlirumeX

sweererlirumeX

Skilled2021-08-21Added 91 answers

(6+i)(x+yi)=2
6x+xi+6yi+yi2=2
Substitute i2=1:
6x+xi+6yiy=2
(6xy)+(x+6y)i=2
Since 2=2+0i, it's appropriate to equate the real parts and the imaginary parts of each side to obtain 2 equations:
6xy=2 (a)
x+6y=0 (b)
Multiply (a) by 6:
36x6y=12 (c)
Add (b) and (c) to solve for x:
37x=12
x=1237
Use (a) to solve for y:
6×1237y=2
y=27237
y=(237)

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