Question

1. Simplify the complex number expression and leave in standard form:

-5(1+2i)+3i(3-4i)

Answer 1

7 - i

Explanation:

Standard form of a complex number is a + bi. The a represents the real part and bi represents the imaginary part.

Keep in mind that i^2 = -1.

To simplify this complex number expression first distribute -5 inside the parentheses.

-5(1 + 2i) ⇒ -5 - 10i

Now distribute 3i inside the parentheses.

3i(3 - 4i) ⇒ 9i - (-12)

Put both of these expressions together and combine like terms as normal.

-5 - 10i + 9i + 12

-5 + 12 = 7

-10i + 9i = -i

We are left with 7 - i as our answer. This is already in standard form of a complex number, therefore, it is our final answer.