Perform the indicated operation. 2i(3-4i)+8(4-5i)(4+5i)

336+6i

The key to solving this problem is to choose which parts you should solve first.

2i(3-4i)+8(4-5i)(4+5i)

let's divide this expression to three parts:

2i(3-4i), 8 and (4-5i)(4+5i)

first let's solve 2i(3-4i):

2i(3-4i) =

2i × 3 + 2i × -4i =

6i - 8i² =

6i + 8

(4-5i)(4+5i):

(4-5i)(4+5i) =

16 + 20i - 20i -25² =

16 + 25 =

41

8(4-5i)(4+5i):

8(4-5i)(4+5i) = 8 × 41 = 328

Now let's put back these parts:

2i(3-4i)+8(4-5i)(4+5i) =

6i + 8 + 328 =

6i +336 OR 336 +6i