Answer:
(21 + √50) - (3√10 - 7√5)i
Explanation:
Step 1: Recognize that you are working with complex numbers, and you will need to use the properties of the imaginary unit, denoted as "i," where i = √(-1).
Step 2: Rewrite the expression with i values:
(3 + √(-5))(7 - √(-10)) = (3 + i√5)(7 - i√10)
Step 3: Apply the distributive property to multiply the two binomials. You can use the FOIL (First, Outer, Inner, Last) method for this. Multiply the first terms, the outer terms, the inner terms, and the last terms:
(3 + i√5)(7 - i√10) = 3 * 7 + 3 * (-i√10) + i√5 * 7 - i√5 * (-i√10)
Step 4: Simplify each term:
3 * 7 = 21
3 * (-i√10) = -3√10i
i√5 * 7 = 7i√5
-i√5 * (-i√10) = √5√10 = √50
So, the expression becomes:
21 - 3√10i + 7i√5 + √50
Step 5: Combine like terms. In this case, combine the terms with "i" and the real number terms separately:
(21 + √50) + (-3√10i + 7i√5)
Step 6: Express the result in standard form, which is a + bi, where "a" and "b" are real numbers:
a = 21 + √50
b = -3√10 + 7√5
So, the expression in standard form is:
(21 + √50) - (3√10 - 7√5)i