# Determine the value of a and b if 3a + 2i = (3 + 4bi)^2

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The value of a and b has to be determined given that 3a + 2i = (3 + 4bi)^2

3a + 2i = (3 + 4bi)^2

=> 3a + 2i = 9 - 16b^2 + 24bi

equate the real and complex coefficients

=> 9 - 16b^2 = 3a and 2 = 24b

=> b = 1/12

3a = 9 - 16/144 = 80/9

=> a = 80/27

**The value of a = 80/27 and b = 1/12**