Subtract $(3+9 i)$ from $(-2+17 i)$.
Answer (1)
Subtract the real parts: − 2 − 3 = − 5 .
Subtract the imaginary parts: 17 i − 9 i = 8 i .
Combine the results to get the complex number: − 5 + 8 i .
The final answer is − 5 + 8 i .
Explanation
Understanding the Problem We are asked to subtract the complex number ( 3 + 9 i ) from the complex number ( − 2 + 17 i ) . This means we need to perform the operation ( − 2 + 17 i ) − ( 3 + 9 i ) .
Performing the Subtraction To subtract complex numbers, we subtract the real parts and the imaginary parts separately. So, we have:
Real part: − 2 − 3 = − 5 Imaginary part: 17 i − 9 i = 8 i
Combining Real and Imaginary Parts Combining the real and imaginary parts, we get the result: − 5 + 8 i .
Final Answer Therefore, the result of subtracting ( 3 + 9 i ) from ( − 2 + 17 i ) is − 5 + 8 i .
Examples
Complex numbers are used in electrical engineering to represent alternating current (AC) circuits. The voltage and current in an AC circuit can be represented as complex numbers, and operations like subtraction can be used to analyze the behavior of the circuit. For example, subtracting two complex voltages can help determine the voltage drop across a component in the circuit. This allows engineers to design and analyze AC circuits more effectively.
