What is the conjugate of 5- square root 3?

Answer 1

2

Answer 2

When a conjugate is multiplied by the original number it removes the surd (or in the case of complex numbers, the complex conjugate removes the imaginary part of the number); this is usually done with a fraction with a surd (or complex number) in a denominator - both numerator and denominator are multiplied by the conjugate. To do this replace a plus by a minus, or a minus by a plus.

Thus (5 - √3) would become either (5 + √3) or (-5 - √3), though it is usual to change the sign of the surd. When multiplied together, they become the difference of two squares; depending upon which sign is changed the result is either positive or negative:

(5 - √3)(5 + √3) = 5² - (√3)² = 25 - 3 = 22

(5 - √3)(-5 - √3) = (5 - √3)((5 + √3) × -1) = ((5 - √3)(5 + √3)) × -1 = (5² - (√3)²) × -1 = 22 × -1 = -22.

Answer 3

The conjugate of a complex number is obtained by changing the sign of the imaginary part. In this case, the complex number is 5 - √3. Therefore, the conjugate of 5 - √3 is 5 + √3. The conjugate pairs have the same real part but opposite imaginary parts, which helps simplify operations involving complex numbers.

Answer 4

The idea is to simply replace the minus by a plus. Or, if there is a plus, replace it by a minus.

Answer 5

The conjugates are 5 + sqrt(3) or -5 - sqrt(3). Just change one of the signs.