%5E2.jpeg "(8i)^2")
Understanding (8i)^2
This expression involves the imaginary unit i, which is defined as the square root of -1 (√-1). Let's break down how to simplify (8i)^2:
Applying the Exponent
Remember that squaring a term means multiplying it by itself:
(8i)^2 = (8i) * (8i)
Multiplication of Complex Numbers
To multiply complex numbers, we distribute as we would with regular binomials:
(8i) * (8i) = 8 * 8 * i * i = 64 * i^2
The Key: i^2 = -1
Since i is the square root of -1, squaring it results in -1:
i^2 = (√-1)^2 = -1
Final Simplification
Substituting i^2 with -1 in our expression:
64 * i^2 = 64 * (-1) = -64
Therefore, (8i)^2 = -64.
This demonstrates that squaring an imaginary number results in a real number.