What is the sum of $12-5 i$ and $-3+4 i$?

Add the real parts: 12 + ( − 3 ) = 9 .
Add the imaginary parts: − 5 i + 4 i = − i .
Combine the real and imaginary parts: 9 − i .
The sum of the complex numbers is 9 − i ​ .

Explanation

Understanding the Problem We are asked to find the sum of two complex numbers, 12 − 5 i and − 3 + 4 i . To do this, we add the real parts together and the imaginary parts together.

Adding Real Parts First, let's add the real parts: 12 + ( − 3 ) = 9 .

Adding Imaginary Parts Next, let's add the imaginary parts: − 5 i + 4 i = − i .

Combining Results Combining these results, we get 9 − i .

Final Answer Therefore, the sum of 12 − 5 i and − 3 + 4 i is 9 − i .


Examples
Complex numbers are used in electrical engineering to represent alternating currents. The sum of complex impedances in a circuit can be calculated using complex number addition, similar to the problem we solved. This helps engineers analyze and design electrical circuits efficiently.

Answered by GinnyAnswer | 2025-07-03

The sum of the complex numbers 12 − 5 i and − 3 + 4 i is 9 − i . This is calculated by adding the real parts (12 and -3) and adding the imaginary parts (-5i and 4i) separately before combining the results. Thus, the final answer is 9 − i .
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Answered by Anonymous | 2025-07-04