Question

Identify the product in the form a bi. (−1 i)(1 − i)

Answer 1

After distributing and multiplying the terms of the complex numbers (−1 i) and (1 − i), we combine like terms to get the final product in the form a bi, which is −2 + 2i.

Step-by-step explanation:

To identify the product in the form a bi, we need to multiply the two complex numbers (−1 i) and (1 − i). Let's perform the multiplication step by step:

Distribute each term in the first complex number by each term in the second complex number, similar to how you would with binomials.

First, multiply −1 by 1, which gives −1.

Then, multiply −1 by −i, which gives i.

Next, multiply i by 1, which gives i.

Finally, multiply i by −i. Since i*i = i^2, and we know that i^2 = −1, this gives −1.

Combine the real numbers and imaginary numbers separately. So, we have the real part −1 − 1, which is −2, and the imaginary part i + i, which is 2i.

The final product in the form a bi is therefore −2 + 2i.

Answer 2

The product in the form a + bi is -1 - i. In order to find the product in the form a + bi, we can use the FOIL method to expand the given expression: (-1i)(1 - i) = -i + i^2 = -i - 1 = -1 - i.

Step-by-step explanation:

In order to find the product in the form a + bi, we can use the FOIL method to expand the given expression: (-1i)(1 - i) = -i + i^2 = -i - 1 = -1 - i.

Consequently, the product is expressed as -1 - i.

This outcome represents a complex number in the standard form, where a is the real part and bi is the imaginary part.

In this case, _1 corresponds to the real part, and −i signifies the imaginary part.

Utilizing the combination of the FOIL method and the properties of imaginary units, we efficiently determine the product of the given complex numbers in the desired form a+ bi facilitating a clear representation of the result in terms of both real and imaginary components.