Math Problem Statement
1-i / 2i
Solution
The given expression is , where represents the imaginary unit. Let's simplify it step by step.
Step 1: Multiply by the conjugate of the denominator
To eliminate the imaginary part in the denominator, multiply both the numerator and denominator by the conjugate of , which is :
Step 2: Simplify the denominator
So the denominator becomes .
Step 3: Simplify the numerator
Now, expand the numerator:
Since , the numerator simplifies to:
Step 4: Combine the results
Now, the expression is:
Thus, the simplified form of is:
Would you like a more detailed explanation or have any questions?
Here are 5 related questions to explore further:
- How do you multiply complex numbers?
- What is the geometric interpretation of multiplying by ?
- How do you find the conjugate of a complex number?
- How do you divide complex numbers in polar form?
- Can you explain the properties of imaginary numbers?
Tip: When dividing complex numbers, always multiply by the conjugate to simplify the expression.
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Math Problem Analysis
Mathematical Concepts
Complex Numbers
Conjugates
Imaginary Unit
Formulas
i^2 = -1
Conjugate of a complex number: a + bi -> a - bi
Multiplying complex numbers: (a+bi)(c+di) = ac + adi + bci + bdi^2
Theorems
Properties of the Imaginary Unit
Conjugate Multiplication
Suitable Grade Level
Grades 10-12