Conjugates of radical & complex numbers
CONCEPTS
Conjugates
• Use the conjugate whenever there is a radical or a square root (or complex number) in the denominator
• Multiply the conjugate by the numerator and denominator to remove the radical (or complex number) out of the denominator
• The conjugate takes the following form
• 5 / (x – √y) => the conjugate is (x + √y)
• 5 / (√y + 9) => first put it into standard form, 5 / (9 + √y) and the conjugate is (9–√y)
PRACTICE PROBLEMS
Question 1 If 5 + 3i is a complex expression, what is required for it to be multiplied by to make it a real expression?
-- Answer -- 5 - 3i
The imaginary part of the expression goes away when a complex number expression is multiplied by it’s conjugate.
Question 2 Reduce 25x / (x - √5)
-- Answer -- (25x² + 25x * √5) / (x² -5)
25x / (x - √5) -> the conjugate of x - √5 is x + √5
25x (x + √5) / ((x - √5)(x + √5)) = (25x² + 25x * √5) / (x² - 5)
ACT PRACTICE PROBLEMS
