SOLUTION: Can you please answer this question for finding the complex number z = x + yi that satisfies the equation (1+3i)z + (4-2i)z = 10+4i Thank you so much if you help!!

Question 1081986: Can you please answer this question for finding the complex number z = x + yi that satisfies the equation (1+3i)z + (4-2i)z = 10+4i
Thank you so much if you help!!
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
(1+3i)z + (4-2i)z = 10+4i
:
factor z on left side of =
:
z(1+3i +4-2i) = 10+4i
:
z(5+i) = 10+4i
:
divide both sides of = by (5+i)
:
z = (10+4i) / (5+i)
:
multiply the numerator and denominator by (5-i)
:
z = ((10+4i)*(5-i)) / ((5+i)*(5-i))
:
z = (10+4i)*(5-i) / 26
:
Note that -i^2 = -(-1) = 1
:
(10+4i) and 26 are divisible by 2
:
z = (5+2i)*(5-i) / 13
:
z = (25+10i-5i-2i^2) / 13
:
*****************
z = (27+5i) / 13
*****************
:

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