Math Problem Statement
(1+2i)(2-3i)/((2-i)(3+2i))
Solution
To solve the given expression:
we'll simplify the numerator and denominator separately, then simplify the overall expression.
Step 1: Simplifying the numerator
We can expand this by using the distributive property (FOIL):
Simplify:
Recall that , so:
Thus, the numerator simplifies to:
Step 2: Simplifying the denominator
Again, we expand using the distributive property:
Simplify:
Using :
Thus, the denominator simplifies to:
Step 3: Putting it together
Now we can rewrite the entire expression:
Since both the numerator and denominator are the same, the expression simplifies to:
Final Answer:
Would you like a detailed breakdown of any specific step? Or have any other questions related to complex numbers?
Here are 5 related questions to explore:
- How do you handle the multiplication of complex numbers using polar form?
- Can you explain how to divide complex numbers using conjugates?
- What happens if you multiply a complex number by its conjugate?
- What is the geometric interpretation of multiplying complex numbers?
- How can you represent complex numbers on the complex plane?
Tip: When multiplying or dividing complex numbers, always remember to use the distributive property carefully and simplify as .
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Math Problem Analysis
Mathematical Concepts
Complex Numbers
Multiplication of Complex Numbers
Division of Complex Numbers
Simplification of Expressions
Formulas
(a+bi)(c+di) = (ac-bd) + (ad+bc)i
(a+bi)/(c+di) = ((a+bi)(c-di))/((c+di)(c-di))
Theorems
Multiplying Complex Numbers
Division of Complex Numbers using Conjugates
Suitable Grade Level
Grades 9-12