Simplify

Problem

(√(,3)+√(,15)*i)*(√(,3)−√(,15)*i)

Solution

1. Identify the expression as a product of conjugates in the form (a+b*i)*(a−b*i)

2. Apply the formula for the product of complex conjugates, which is (a+b*i)*(a−b*i)=a2+b2

3. Substitute the values a=√(,3) and b=√(,15) into the formula.

4. Square the terms to eliminate the radicals.

(√(,3))2=3

(√(,15))2=15

5. Add the resulting values.

3+15=18

Final Answer

(√(,3)+√(,15)*i)*(√(,3)−√(,15)*i)=18

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