Math Problem Statement
Find the values of x and y that make the equation true.
5+y+(3x−7)i=9−3i
List the value of x and then the value of y, separated by a comma.
Solution
To solve the equation , we can separate the real and imaginary parts and equate them individually.
Step 1: Separate real and imaginary parts.
The given equation is:
- The real part is .
- The imaginary part is .
On the right-hand side:
- The real part is .
- The imaginary part is .
Step 2: Equate the real parts.
Equating the real parts:
Solve for :
Step 3: Equate the imaginary parts.
Equating the imaginary parts:
Solve for :
Final answer:
The values of and that make the equation true are:
Thus, and are .
Do you want further details or have any questions? Here are 5 related questions to explore:
- How can you solve similar equations involving complex numbers?
- What is the importance of separating real and imaginary parts in equations?
- How do you solve linear equations involving imaginary terms?
- Can you explain the properties of imaginary numbers in algebra?
- How would the solution change if the imaginary terms were more complex?
Tip: Always separate real and imaginary parts in complex number equations to simplify solving.
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Math Problem Analysis
Mathematical Concepts
Algebra
Complex Numbers
Equating Real and Imaginary Parts
Formulas
Equating real and imaginary parts of a complex number equation
Theorems
Equality of complex numbers
Suitable Grade Level
Grades 9-12
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