Math Problem Statement
Diketahui (x + 3i) × (2 - 2i) = 4 + 8i. Nilai 3x adalah ...
Solution
To solve the equation:
Step 1: Expand the left-hand side
Using the distributive property:
Recall that , so:
This simplifies to:
Group real and imaginary terms:
Step 2: Set the real and imaginary parts equal
The equation becomes:
From the real part:
From the imaginary part:
Step 3: Solve for
From the real part:
Check the imaginary part:
Thus, .
Step 4: Calculate
Final Answer:
Let me know if you'd like more details or have further questions! Here are some related questions to explore:
- How is derived and used in complex number calculations?
- What is the geometric interpretation of multiplying complex numbers?
- How do you simplify complex number expressions?
- What are some applications of complex numbers in engineering or physics?
- How can you solve similar equations with unknowns in both parts of a complex number?
Tip: Always separate real and imaginary parts carefully to avoid errors when solving complex equations.
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Math Problem Analysis
Mathematical Concepts
Complex Numbers
Algebra
Distributive Property
Formulas
(a + bi)(c + di) = (ac - bd) + (ad + bc)i
Theorems
Properties of Complex Numbers
Suitable Grade Level
Grades 10-12