#(2x+y)+(3x-4y)i=(x-2)+(4y-5)i# Find x and y..?

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Answer 1 · 2018-05-12T16:05:00

#x=-21/11,y=-1/11#

We have

#(2x+y)+(3x-4y)i=(x-2)+(4y-5)i#

We know two complex numbers #a+bi# and #c+di# iff #a=c# and #b=d#. So, in this case, we must have

#2x+y=x-2#

#3x-4y=4y-5#

so

#x=-y-2#

#3(-y-2)-4y=-3y-6-4y=-7y-6=4y-5#

so #11y=-1# and #y=-1/11#

Hence, #x=1/11-2=1/11-22/11=-21/11#

We make a quick check:

#2(-21/11)-1/11=-43/11#

#-21/11-2=-21/11-22/11=-43/11#

So, our values of #x# and #y# are correct.