Q. Express the radical using the imaginary unit, i.Express your answer in simplified form.±−20=±□
Rephrasing and recognizing: First, let's rephrase the "Express the radical using the imaginary unit, i, and simplify the expression ±−20."
Separating the square root: Recognize that the square root of a negative number involves the imaginary unit i, where i2=−1. We can express ±−20 as ±−1×20.
Replacing −1 with i: Separate the square root of the product into the product of square roots, knowing that a⋅b=a⋅b. This gives us ±−1⋅20.
Simplifying 20: Replace −1 with i, since they are equivalent. This transforms the expression into ±i⋅20.
Taking the square root of 4: Simplify 20 by factoring it into 4×5, since 4 is a perfect square and its square root can be easily calculated.
Combining constants outside the radical: Take the square root of 4, which is 2, and bring it outside the radical. This leaves us with ±i⋅2⋅5.
Combining constants outside the radical: Take the square root of 4, which is 2, and bring it outside the radical. This leaves us with ±i⋅2⋅5.Combine the constants outside the radical to simplify the expression. This results in ±2i⋅5.
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