$(13+4i) + n = 0$. What is $n$?
Answer (1)
Isolate n in the equation ( 13 + 4 i ) + n = 0 .
Subtract ( 13 + 4 i ) from both sides: n = − ( 13 + 4 i ) .
Distribute the negative sign: n = − 13 − 4 i .
The solution is − 13 − 4 i .
Explanation
Understanding the Problem We are given the equation ( 13 + 4 i ) + n = 0 , where i is the imaginary unit, and we need to find the value of n .
Isolating n To find n , we need to isolate it on one side of the equation. We can do this by subtracting ( 13 + 4 i ) from both sides of the equation: ( 13 + 4 i ) + n − ( 13 + 4 i ) = 0 − ( 13 + 4 i ) n = − ( 13 + 4 i )
Distributing the Negative Sign Now, we distribute the negative sign to both the real and imaginary parts: n = − 13 − 4 i
Final Answer Therefore, the value of n that satisfies the equation is − 13 − 4 i .
Examples
In electrical engineering, complex numbers are used to represent alternating current (AC) circuits. If the total impedance of a circuit is represented by 13 + 4 i and you want to neutralize it (make the total impedance zero), you would need to add an impedance of − 13 − 4 i . This ensures that the circuit operates efficiently without any reactive components.
