(2i)^(5)*(i Sqrt(6))^(2)

Jasonbradley

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Jun 16, 2024

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Simplifying Complex Expressions: (2i)^(5)*(i√6)^(2)

This article will guide you through simplifying the complex expression (2i)^(5)*(i√6)^(2).

Understanding Complex Numbers

Complex numbers are numbers that can be expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit, defined as the square root of -1.

Simplifying the Expression

1. Simplify the powers:

   • (2i)^(5) = 2^5 * i^5 = 32 * i^5
   • (i√6)^(2) = i^2 * (√6)^2 = -1 * 6 = -6

2. Simplify i^5:

   • i^5 = i^4 * i = (i^2)^2 * i = (-1)^2 * i = i

3. Combine the simplified terms:

   • 32 * i * -6 = -192i

Final Result

Therefore, the simplified form of (2i)^(5)*(i√6)^(2) is -192i.