Write the conjugate of the following..

Question

anonymous · Answer

$$2+3 \iota$$

anonymous · Answer

@campbell_st

campbell_st · Answer

well isn't the conjugate 2 - 3i

anonymous · Answer

Can u exlain to me what a conjugate is

campbell_st · Answer

complex roots to polynomials occur in pairs

so 2 + 3i is one root.... the conjugate is 2 - 3i

which means to solution to a quadratic could have been 

$$(x -2)^2 = -9$$

so the values that x can take are 

$$x - 2 = \pm\sqrt{-9}$$

because

$$(-\sqrt{-9})^2 = (\sqrt{-9})^2 = -9$$

then the solution is 

$$x = 2 \pm \sqrt{-9}$$

and substituting i^2 = -1

you get 

$$x = 2 \pm \sqrt{9i^2} = 2 \pm 3i$$

so if 2 + 3i is a solution the other is 2 - 3i

hope it makes sense.... but if you take the square root of something there are 2 possible solutions, the positive and negative case

hope it makes sense