Final answer:
To simplify the expression (√24+√2/4i)², we can start by simplifying the square root of 24 and the square root of 2. The expression simplifies to 24 + (√3/2i).
Step-by-step explanation:
To simplify the expression (√24+√2/4i)², we can start by simplifying the square root of 24 and the square root of 2. The square root of 24 can be expressed as 2√6, and the square root of 2 can be left as it is.
So, the expression becomes (2√6 + √2/4i)².
To square this expression, we can use the formula (a + b)² = a² + 2ab + b². In this case, a is 2√6 and b is √2/4i.
Using the formula, we get (2√6)² + 2(2√6)(√2/4i) + (√2/4i)².
Simplifying further, we get 4(√6)² + 4(√6)(√2/4i) + (√2/4i)².
The square of √6 is 6, and the square of (√2/4i) is -1/4.
So, the final expression is 24 + (√6)(√2/2i) + (-1/4).
To express it in the simplest form, we can write it as:
24 + (√3/2i)