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

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2 Answers

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
(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