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Find the value of a and b if (a-2)+3bi=7+6i

This is for my math analysis class, and I can't quite figure out how to do it!

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Eric O. | Algebra 1, 2, Geometry, Pre-Calculus, CalculusAlgebra 1, 2, Geometry, Pre-Calculus, Ca...
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Make the real component on the left side equal to the real component on the right.
 
a-2=7 therefore,
a=9
 
Make the imaginary component on the left side equal to the imaginary component on the right.
 
3bi=6i
b=2
 
Plug them and get
7+6i=7+6i
Steve S. | Tutoring in Precalculus, Trig, and Differential CalculusTutoring in Precalculus, Trig, and Diffe...
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(a-2) + (3b)i = (7) + (6)i
 
The left real part = the right real part: a - 2 = 7, a = 9
 
The left imaginary part = the right imaginary part: 3b = 6, b = 2