Complex Numbers

Question

Determine the product of the given complex number.

a) -1/2+1/2√3i, -1/2-1/2√3i

b)-1/2+1/2√3i, -1/2+1/2√3

c)-1/2-1/2√3i, -1/2-1/2√3

 

I have found an answer for each one,

a) 1

b)-(1+√3i)/2

c)-(1-√3i)/2

 

However, I am iffy about these answers, doing them again, I got a couple of different answers... Please Help :s

 

Answer 1

I would multiply them out using FOIL method.  Then combining like terms.  I will do the first one for you.

 

(-0.5 + 0.5√(3i)) * (-0.5 - 0.5√(3i))

 

Notice that this will turn out to be a difference in perfect squares, since you are multiplying a complex number by its conjugate.

 

(1/4) - (1/4)(3i) =

 

(1/4)(1 - 3i)

 

 

Try the others on your own.