Question
Question: How do you simplify \[{{i}^{752}}\]?...
How do you simplify i752?
Solution
In this problem, we have to simplify the given imaginary part. We should know that any negative terms inside the square root is equal to an imaginary part, which will be a complex number. We can write it as i=−1. Using this we can find the value of i4. We can then split the given power term in terms of multiplication of 4 to find the value of the given imaginary part.
Complete step by step solution:
We know that the given imaginary part to be simplified is i752.
We know that any negative terms inside the square root is equal to an imaginary part, which will be a complex number.
We can write it as,
i=−1.
We can now write the square term of i, we get
⇒i2=(−1)2=−1
We can now write the fourth power of i, using the above step, we get