Question

Complete each of the following statements given z = 1 – 2i and w = –3 5i. What is the value of z w?

1) -2i
2) -8 + 7i
3) 7i
4) -8 - 7i

Answer 1

The product of the complex numbers z = 1 - 2i and w = -3 + 5i is calculated to be 7 + 11i, using the distributive property to combine like terms. Therefore, the correct answer to the question is not given in the provided options.

Step-by-step explanation:

The question involves complex number multiplication and asks what the product of complex numbers z and w is, where z = 1 − 2i and w = −3 + 5i. To find the product, we multiply the complex numbers just as we would with binomials:

zw = (1 − 2i)(−3 + 5i)

First, we'll use the distributive property to multiply each term in the first complex number by each term in the second complex number:

1. (1)(-3) = -3
2. (1)(5i) = 5i
3. (-2i)(-3) = 6i
4. (-2i)(5i) = -10i2

Recall that i2 = -1, so -10i2 becomes +10. Combine the real components (-3 and +10) and the imaginary components (5i and 6i):

zw = -3 + 10 + 5i + 6i

This simplifies to:

zw = 7 + 11i

Therefore, the correct answer is none of the options provided in the question. The value of zw is 7 + 11i.