Question

3i + 2i - 4 = 18i

No solution, infinite solutions, one

Answer 1

To determine the number of solutions for the equation \( 3i + 2i - 4 = 18i \), we can start by simplifying the left side.

1. Combine the like terms on the left side:
\[
(3i + 2i) - 4 = 5i - 4
\]

So our equation now looks like this:
\[
5i - 4 = 18i
\]

2. Next, we can move all terms involving \(i\) to one side of the equation. Subtract \(5i\) from both sides:
\[
-4 = 18i - 5i
\]
\[
-4 = 13i
\]

3. Now, solve for \(i\):
\[
i = \frac{-4}{13}
\]

Since we found a specific value for \(i\), this means the equation has a **unique solution**.

**Therefore, the answer is: one solution.**