Let $$u = 2 - 3i \text { and } v = -3 +i.$$ Which of the following is the Cartesian form of the complex number $u + uv$?

Question

BlackTom AI · Accepted Answer

The problem asks for the Cartesian form of the complex number u + uv, given u = 2 - 3i and v = -3 + i.

First, compute the product uv:
- Multiply (2 - 3i) by (-3 + i):
  (2)(-3) + (2)(i) + (-3i)(-3) + (-3i)(i) = -6 + 2i + 9i - 3i^2.
- Since i^2 = -1, the term -3i^2 becomes -3(-1) = +3.
- Combine real parts and imaginary parts: (-6 + 3) + (2i + 9i) = -3 + 11i.

Next, add u to uv to get u + uv:
- u + uv = (2 - 3i) + (-3 + 11i) = (2 - 3) + (-3i + 11i) = -1 + 8i.

Thus, the Cartesian form of u + uv is -1 + 8i.

Note: The provided data shows an answer value (-1 + 8i) but the list of answer options is empty. This means there are no listed choices to select from in the given options field, even though the computed result is -1 + 8i. If options were available, the correct option would be the one matching -1 + 8i.

Let \[u = 2 - 3i \text { and } v = -3 +i.\] Which of the following is the Cartesian form of the complex number \(u + uv\)?Single choice

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