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 i⁹³
𝐒𝐨𝐥𝐮𝐭𝐢𝐨𝐧:
To evaluate i^93, we need to find the remainder when the exponent 93 is divided by 4.
93 ÷ 4 = 23 with a remainder of 1.
So, i^93 is equivalent to i^1.
i^1 = i
Therefore, i^93 = i.