Question

Complete each of the following statements given z = 1 – 2i and w = –3 + 5i.

a. z w = −2 + i
b. z − w = –7i
c. w − z = –4 + i
d. All of the above

Answer 1

The given complex number calculations for zw, z − w, and w − z with z = 1 − 2i and w = −3 + 5i do not match any of the presented options in the question. Therefore, the correct response is 'none of the above'.

Step-by-step explanation:

To complete each of the statements with complex numbers z = 1 − 2i and w = −3 + 5i, we perform the following calculations:

• For the product, zw, we calculate (1 − 2i)(−3 + 5i) = −3 + 5i − 6i + 10i². Since i² = −1, the result is −3 + 5i − 6i − 10 = −13 − i, which is not −2 + i.
• For the difference z − w, we calculate (1 − 2i) − (−3 + 5i) = 1 − 2i + 3 − 5i = 4 − 7i, which is not −7i.
• For the difference w − z, we calculate (−3 + 5i) − (1 − 2i) = −3 + 5i − 1 + 2i = −4 + 7i, which is not −4 + i.

Therefore, none of the given statements a, b, or c are correct when using the complex numbers provided.