How do you solve #2ix - 5 + 3i = (2 - i)x + i#?

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Answer 1 · 2015-12-05T20:06:47

#x=((-16-11i))/(5)#

Given: #2ix-5+3i=(2-i)x+i#

Multiply out the brackets

#2ix-5+3i=2x-ix+i#

Collecting like terms

#(2ix+ix)+(3i-i)-2x-5=0#

#x(3i)+2i-2x-5=0#

#x(-2+3i)+(-5+2i)=0#

#x=((5-2i))/((-2+3i))......................(1)#

Using #(a^2-b^2)=(a-b)(a+b)#
Multiply equation (1) by 1 in the form of #((-2-3i))/((-2-3i))#

#x=((5-2i)(-2-3i))/((-2+3i)(-2-3i)) color(white)(..)=color(white)(..)(-16-11i)/(5)#