Question

Evaluate the expression (-7- 5i)(5 – 4i) and write the result in the form a + bi.

Answer 1

To evaluate the expression (-7- 5i)(5 – 4i) and write the result in the form a + bi, multiply the two complex numbers using the distributive property. The final result is -15 + 3i.

Step-by-step explanation:

To evaluate the expression (-7- 5i)(5 – 4i) and write the result in the form a + bi, we need to multiply the two complex numbers using the distributive property. Distributing the -7-5i to both terms inside the parentheses, we get (-7)(5) + (-7)(-4i) + (-5i)(5) + (-5i)(-4i). Simplifying each term, we have:

-35 + 28i - 25i - 20i^2.

Now, substitute i^2 with -1 and combine like terms. The final result is:

-35 + 3i - 20(-1) = -15 + 3i.