Step 1 :Given the complex division problem \(\frac{-8+6i}{4+2i}\), we need to simplify it to the form \(a+bi\).
Step 2 :To do this, we multiply the numerator and the denominator by the conjugate of the denominator. The conjugate of a complex number is obtained by changing the sign of its imaginary part. So, the conjugate of the denominator \(4+2i\) is \(4-2i\).
Step 3 :Multiplying the numerator by the conjugate, we get \((-8 + 6i)(4 - 2i)\).
Step 4 :Multiplying the denominator by its conjugate, we get \((4 - 2i)(4 + 2i)\).
Step 5 :Simplifying these expressions, we get the result \(\frac{-8 + 6i}{4 + 2i} = -1 + 2i\).
Step 6 :So, the quotient in the form \(a+bi\) is \(\boxed{-1+2i}\).