To simplify \((2i)^4\), follow these steps:

1. Calculate the power of the imaginary unit \(i\):
\[ i^4 = (i^2)^2 = (-1)^2 = 1 \]

2. Calculate the power of the coefficient \(2\):
\[ (2)^4 = 16 \]

3. Combine the results:
\[ (2i)^4 = 16 \cdot i^4 = 16 \cdot 1 = 16 \]

Therefore, \((2i)^4\) simplifies to \(16\).

Would you like more details or have any questions?

Here are some related questions for further exploration:
1. What are the properties of the imaginary unit \(i\)?
2. How do you multiply complex numbers?
3. What is the result of \((3i)^3\)?
4. How do you divide complex numbers?
5. How do you add and subtract complex numbers?
6. How do you find the modulus of a complex number?
7. What is the polar form of a complex number?
8. How do you find the roots of complex numbers?

**Tip:** Remember that \(i\) is defined as \(\sqrt{-1}\), and its powers cycle every four: \(i, -1, -i, 1\). This can help you quickly simplify expressions involving \(i\).

Learn how to simplify (2i)^4 using a detailed step-by-step solution. Understand the properties of imaginary numbers and exponents. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation