Math Problem Statement

(2i)^4 simplified

Solution

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

  1. Calculate the power of the imaginary unit ii: i4=(i2)2=(1)2=1i^4 = (i^2)^2 = (-1)^2 = 1

  2. Calculate the power of the coefficient 22: (2)4=16(2)^4 = 16

  3. Combine the results: (2i)4=16i4=161=16(2i)^4 = 16 \cdot i^4 = 16 \cdot 1 = 16

Therefore, (2i)4(2i)^4 simplifies to 1616.

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 ii?
  2. How do you multiply complex numbers?
  3. What is the result of (3i)3(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 ii is defined as 1\sqrt{-1}, and its powers cycle every four: i,1,i,1i, -1, -i, 1. This can help you quickly simplify expressions involving ii.

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Math Problem Analysis

Mathematical Concepts

Complex Numbers
Powers and Exponents

Formulas

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Theorems

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Suitable Grade Level

Grades 9-12