Math Problem Statement
Perform the indicated operation & simplify. Express the answer in terms of i (as a complex number). (9+7i)(5+2i)
Solution
We need to perform the multiplication and simplify the result.
Step 1: Apply the distributive property (FOIL method)
We distribute each term in the first binomial to each term in the second binomial:
This simplifies to:
Step 2: Simplify the result
- Combine the real parts:
- Combine the imaginary parts:
- Simplify . Since , we have:
Now, put it all together:
This simplifies to:
Final Answer:
Would you like more details on this process, or do you have any other questions?
Further Questions:
- What is the general rule for multiplying two complex numbers?
- How do we handle complex conjugates in multiplication?
- Can we factorize the expression further?
- How do we add or subtract complex numbers?
- What is the geometric interpretation of multiplying complex numbers?
Tip: When multiplying complex numbers, always remember to use the fact that , which can help
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Complex Numbers
Algebra
Multiplication of Binomials
Formulas
(a + bi)(c + di) = ac + adi + bci + bdi^2
i^2 = -1
Theorems
Properties of Complex Numbers
Distributive Property
Suitable Grade Level
Grades 9-12