To simplify the expression \( 3 + 2i - 7 = 15 \), start by combining the real numbers:
- Combine the real parts: \[ 3 - 7 = -4 \]
So the expression simplifies to: \[ -4 + 2i = 15 \]
Next, we can isolate \( 2i \) by moving \( -4 \) to the right side: \[ 2i = 15 + 4 \] \[ 2i = 19 \]
Now, if you divide by 2 to solve for \( i \): \[ i = \frac{19}{2} \]
Thus, the simplified form of the original expression is \( -4 + 2i \) equals \( 15 \), and isolating \( i \) gives us \( i = \frac{19}{2} \).