Perform the operation and get your answer in reduced form of a + bi. (2+i)/(-3-4i) 

Expert Answers
flbyrne eNotes educator| Certified Educator

To divide complex numbers, multiply both numerator and denominator by the conjugate of the denominator.

The conjugate of -3-4i is -3+4i, then

`(2+i)/(-3-4i) * (-3+4i)/(-3+4i)`

Multiply complex numbers as two binomials:





Thus the answer in reduced form is: -0.4+0.2i

Zaca | Student

When there are "i's" in the denominator, the easiest way to get rid of them is to multiply by the conjugate. 

In this case, our expression is:


The congugate is a term to multiply the denominator with to get a perfect square. (Or, to put in simple terms, switch the sign in the middle of the two numbers)

In this case: `(-3+4i)`

Mutiply by the conjugate:

` ` `((2+i)/(-3-4i))*((-3+4i)/(-3+4i))`


`(-6 + 8i -3i -4)/(9-12i+12i+16)`


`(-10 + 5i)/25`

Divide to turn into a + bi form:

`-2/5 + (1/5)i`