4 + (sqrt-4) + i
To evaluate the expression 4 + √(-4) + i, we need to simplify it step by step.
First, let's simplify the square root of -4, which is written as √(-4).
The square root of a negative number is not a real number, but it can be represented as an imaginary number using the imaginary unit "i." The square root of -1 is defined as i.
To find the square root of -4, we can express it as the square root of -1 multiplied by the square root of 4: √(-1) * √4.
√(-1) is equal to "i" and √4 is equal to 2.
So, the square root of -4 can be simplified as 2i.
Now, we can substitute the simplified value of the square root of -4 back into the expression:
4 + 2i + i
Next, combine like terms:
4 + (2 + 1)i
Simplify the real part (the constant term):
4 + 3i
Therefore, 4 + √(-4) + i simplifies to 4 + 3i.