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 i⁸⁸⁸
𝐒𝐨𝐥𝐮𝐭𝐢𝐨𝐧:
To evaluate i^888, we need to find the remainder when the exponent 888 is divided by 4.
888 ÷ 4 = 222 with a remainder of 0.
When the remainder is 0, i^n is equivalent to i^4, which is 1.
Alternatively, since 888 is divisible by 4, i^888 = (i^4)^222 = (1)^222 = 1.
Therefore, i^888 = 1