Question

What is the product of complex numbers (-3i +4) and (3i +4)??? please explain

Answer 1

product of complex numbers (-3i +4) and (3i +4)

(x - y)(x + y) = x² - y²

(-3i +4)(3i +4) = (4 -3i )(4 + 3i) = 4² - (3i)² = 16 - 9*(-1)=16 + 9 = 25

Answer 2

`(-3i+4)*(3i+4)=25`

Explanation:

1. First writhe the complex numbers to multiply:

`(-3i+4)*(3i+4)`

2. Multiply the first term of the first parentheses by the first term of the second parentheses:

`-3i*3i=-9i^(2)`

3. Multiply the first term of the first parentheses by the second term of the second parentheses:

`-3i*4=-12i`

4. Multiply the second term of the first parentheses by the first term of the second parentheses:

`4*3i=12i`

5. Multiply the second term of the first parentheses by the second term of the second parentheses:

4*4=16

6. Write all the terms:

`(-3i+4)*(3i+4)=-9i^(2)-12i+12i+16`

7. Add up the terms:

`(-3i+4)*(3i+4)=-9i^(2)+16`

8. As
`i^(2)=-1`:

`(-3i+4)*(3i+4)=-9(-1)+16\\(-3i+4)*(3i+4)=9+16\\(-3i+4)*(3i+4)=25`