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

Question

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

Answer 1

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

Answer 2

(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