Math Problem Statement
The value of i^146 is equal to ______.
Solution
The question asks for the value of , where is the imaginary unit, defined as .
To solve this, we use the cyclical property of powers of :
To find , we calculate the remainder of 146 when divided by 4: Thus, .
From the cyclical pattern, we know:
Therefore, the value of is , which corresponds to option (B).
Do you want more details or have any questions? Here are five related questions to deepen your understanding:
- How do powers of form a cycle?
- What is the value of ?
- How is the remainder important when dealing with powers of ?
- Can you explain the properties of imaginary numbers?
- How do complex numbers apply to real-world problems?
Tip: For higher powers of , always reduce the exponent modulo 4 to use the repeating pattern.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Complex Numbers
Powers of Imaginary Unit
Formulas
i^1 = i, i^2 = -1, i^3 = -i, i^4 = 1
Theorems
Cyclic Nature of Powers of i
Suitable Grade Level
Grades 9-12