Learn how to simplify expressions involving powers of the imaginary unit 'i'! This video covers several examples, showing you step-by-step how to use the cyclical nature of powers of 'i' to simplify complex number expressions. Perfect for complex number beginners!
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𝐐𝐮𝐞𝐬𝐭𝐢𝐨𝐧: Evaluate i⁴⁰³
𝐒𝐨𝐥𝐮𝐭𝐢𝐨𝐧:
To evaluate i^403, we need to find the remainder when the exponent 403 is divided by 4.
403 ÷ 4 = 100 with a remainder of 3.
So, i^403 is equivalent to i^3.
i^3 = i^2 * i = (-1) * i = -i
Therefore, i^403 = -i.