MATH SOLVE

6 months ago

Q:
# Simplify the following expression into the form a + bi, where a and b are rational numbers. -2i(7-4i)+(3+i)(-2+2i)

Accepted Solution

A:

The answer is -16 - 10i.

Using the distributive property on the first part, we have:

-2i*7--2i*4i + (3+i)(-2+2i)

-14i+8i² +(3+i)(-2+2i)

Using FOIL on the last part,

-14i+8i²+(3*-2+3*2i+i*-2+i*2i)

-14i+8i²-6+6i-2i+2i²

-10i+8i²-6+2i²

Since we know that i = -1,

-10i+8(-1)-6+2(-1)

-10i-8-6-2

-16-10i

Using the distributive property on the first part, we have:

-2i*7--2i*4i + (3+i)(-2+2i)

-14i+8i² +(3+i)(-2+2i)

Using FOIL on the last part,

-14i+8i²+(3*-2+3*2i+i*-2+i*2i)

-14i+8i²-6+6i-2i+2i²

-10i+8i²-6+2i²

Since we know that i = -1,

-10i+8(-1)-6+2(-1)

-10i-8-6-2

-16-10i