How do you solve (-16)^1/4?
By the way is the answer i+2i or i-2i?
in polar coordinates, -16 = (16,pi), so 4th root is (2,pi/4)
so, ∜-16 = √2 + √2 i
What is polar coordinate? I have not learned this yet!
To solve the expression (-16)^(1/4), you need to find the fourth root of -16. Here's the step-by-step process:
Step 1: Find the principal root of the absolute value of the number.
The principal fourth root of 16 is 2 because 2^4 = 16.
Step 2: Determine the four complex roots of the given number.
The four complex roots of -16 are:
- The principal root: 2
- The second root: -2
- The third root: 2i (imaginary unit) (i.e., √(-1))
- The fourth root: -2i
So, (-16)^(1/4) has four solutions: 2, -2, 2i, and -2i.
Keep in mind that when dealing with complex roots, you may need to express the answer in terms of imaginary units (i.e., i).