Simplify the complex numbers: $(-2-4 i)+(1+6 i)$
Answer (1)
Add the real parts: − 2 + 1 = − 1 .
Add the imaginary parts: − 4 i + 6 i = 2 i .
Combine the real and imaginary parts: − 1 + 2 i .
The simplified complex number is − 1 + 2 i .
Explanation
Understanding the problem We are asked to simplify the sum of two complex numbers: ( − 2 − 4 i ) and ( 1 + 6 i ) . To do this, we add the real parts together and the imaginary parts together.
Adding the real parts First, let's add the real parts: − 2 + 1 = − 1
Adding the imaginary parts Next, let's add the imaginary parts: − 4 i + 6 i = 2 i
Combining real and imaginary parts Now, combine the real and imaginary parts to get the simplified complex number: − 1 + 2 i
Examples
Complex numbers are used in electrical engineering to analyze alternating current circuits. They help represent the impedance, which is the opposition to the flow of current in an AC circuit. By using complex numbers, engineers can simplify calculations and design efficient circuits. For example, the voltage and current in a circuit can be represented as complex numbers, and their relationship can be analyzed using complex arithmetic.
