Question

I give medals and fans to people who help me
please

question 1

Part 1: Explain, in complete sentences, the difference between a radical equation and an equation simply containing a radical. (2 points)
Part 2: Provide an example of each. (2 points)

question 2

Part 1: Explain, in complete sentences, the relationship between radicals and complex numbers. (2 points)
Part 2: Give an example illustrating this relationship. (2 points)

Answer 1

In a radical equation, at least one variable of the equation is under a radical sign, or
(equivalently) has a fractional exponent.
Example: sqrt(x+1) = 25
Or (x+1)^(-1/2) = 25 which is the same equation, just expressed differently

An equation with just a radical in it could have the radical (root) of a number or a constant
involved in the terms of the equation.
y^3 +sqrt(A) = sqrt(7) is an example of such an equation, since the variable y does not
have a fractional power (equivalent to having a radical sign over it)

Answer 2

Radicals is the name mathematics uses to define terms under a square root sign.
Complex Numbers take the form a + bi, where a and b are Real Numbers while i represents
the square root of -1

Sq.rt.(x+4) is a radical
[3 + 4(i)] is a Complex Number
Radicals become Complex Numbers whenever the term under the sq.rt. sign is negative.
Thus, sq.rt.(-4) =sq.rt.(4)(sq.rt.(-1), =+/-2i