Express (2 + i)/(4 + i - 3 + 6i) in the form a + bi, where a and b are real numbers.
+23245 First: simplify 4 + i - 3 + 6i = 7i + 1
Then: to simplify (2 + i ) / (7i + 1) multiply both the numerator and denominator by the conjugate of the denominator.
The conjugate of 7i + 1 is 7i - 1.
(2 + i ) / (7i + 1) x (7i - 1) / (7i - 1) = [ (2 + i)(7i - 1) ] / [ (7i + 1)(7i - 1) ]
= ( 13i - 9) / -50
= -(13/50)I + (9/50)
