I just don't know how to solve this problem. I know the answer is 13+i.
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The product is
= 6i + 10 -5i - 3i.i where the imaginary value i = sqrt (i) therefore i.i = -1
= 6i - 5i + 10 - 3(-1)
= i +10 + 3
= 13 + i
I RESEARCHED IT. AN IMAGINARY NUMBER MULTIPLIED BY AN IMAGINARY NUMBER RESULTS IN A NEGATIVE NUMBER. HOWEVER, HEREIN, WE ARE MULTIPLYING (3i)(-i).
i is defined to be sqrt(-1) and is called the imaginary unit.
i^2 = -1
i^3 = i^2 * i = -i
i^4 = i^3 * i = -i * i = - i^2 = - - 1 = 1
i^5 = i^4 * i = 1 * i = i
i^6 = i^5 * i = i * i = i^2 = -1
First use the distributive property:
3i(2-i) +5(2-i) =
6i - 3i^2 +10 - 5i =
Then commutative property of addition and i^2 = -1:
6i - 5i - 3(-1) + 10 =
i + 3 + 10 =
13 + i