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

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flbyrne's profile pic

Posted on

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:

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

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

`=(-10+5i)/25`

`=-0.4+0.2i`

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

Zaca's profile pic

Posted on

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:

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

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))`

Combine: 

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

Simplify:

`(-10 + 5i)/25`

Divide to turn into a + bi form:

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

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