$(9-6 i)
\times m=9-6 i$
What is $m$?
Answer (1)
Divide both sides of the equation by ( 9 − 6 i ) .
Simplify the fraction 9 − 6 i 9 − 6 i .
The result is m = 1 .
Therefore, the value of m is 1 .
Explanation
Understanding the Problem We are given the equation ( 9 − 6 i ) × m = 9 − 6 i and asked to find the value of m . Here, i is the imaginary unit, where i 2 = − 1 .
Isolating m To find m , we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by ( 9 − 6 i ) . This gives us: m = 9 − 6 i 9 − 6 i
Simplifying the Fraction Now, we simplify the fraction. Since the numerator and denominator are the same, the fraction simplifies to 1: m = 1
Final Answer Therefore, the value of m is 1.
Examples
This type of problem, solving for a variable in an equation with complex numbers, is useful in electrical engineering when analyzing AC circuits. Complex numbers are used to represent impedance, and solving for unknowns helps determine circuit behavior. For example, if you have a circuit with a known impedance and voltage, you can use complex numbers to find the current.
