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
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`