Question

Explain, in complete sentences, the effects of multiplying a radical or a complex number by its conjugate. Give an example of each.

Answer 1

The reason we do rationalization or multiply by conjugate is because we don't want a radial or complex number in the denominator. It makes the result somewhat easier to read mathematically.

Answer 2

Suppose you have 2 / i (*i is imaginary number which is sqrt(-1)) you multiply both numerator and denominator by i because i^2 = -1 so you have 2i/-1 = -2i

Answer 3

2/sqrt(2) again you multiply by sqrt(2) for both numerator and denominator to get 2sqrt(2) / 2

Answer 4

If you have something like [(i + 3)] or [sqrt(2) + 5] in the denominator of an algebraic expression, The conjugate will be [(i - 3)[ and [sqrt(2) - 5] respectively its just the same expression with opposite sign.

Answer 5

You will multiply the conjugate both by numerator and denominator as well

Answer 6

\[[2 / (i-3)]x[(i+3)/(i+3); = 2(i + 3)/[i ^{2}-9] = 2(i + 3)/[-10] = -(i+3)/5\]

Answer 7

multiplying a number
\[a+bi\] by its complex conjugate
\[a-bi\] gives \[a^2+b^2\] a real number
for example
\[(4+3i)(4-3i)=4^2+3^2=25\]

Answer 8

multiplying a radical
\[a+\sqrt{b}\] by its conjugate
\[a-\sqrt{b}\] gives
\[a^2-b\] for example
\[(4+\sqrt{3})(4-\sqrt{3})=4^2-3=13\]