Simplify the expression
2+3i/4+3i
To simplify the expression (2+3i)/(4+3i), we can multiply the numerator and denominator by the conjugate of the denominator, which is (4-3i).
[(2+3i)/(4+3i)] * [(4-3i)/(4-3i)]
Expanding the numerator and denominator using the distributive property:
(8-6i+12i-9i^2) / (16-12i+12i-9i^2)
Combining like terms:
(8+6i-9i^2) / (16-9i^2)
Since i^2 is equal to -1:
(8+6i-9(-1)) / (16-9(-1))
Simplifying:
(8+6i+9) / (16+9)
(17+6i) / 25
Therefore, the simplified expression is (17+6i)/25.