Complex numbers help..will give medal and fan

Question

anonymous · Answer

$$\mathbb{C}$$

itiaax · Answer

I need help with this problem..I can't seem to find the right approach as to how to start go about doing it.

Find the value of the real number y such that (3+2i)x(1+yi) is real

anonymous · Answer

multiply out, set the imaginary part equal to zero

anonymous · Answer

i can walk you through it if you like, but that is what it is asking

itiaax · Answer

Can you walk me through it, please?

anonymous · Answer

ok there are two ways to multiply complex numbers, one is to go right to the answer and the other is the more basic way of just multiply like normal and combining like terms

anonymous · Answer

$$(3+2i)(1+yi)=3+3yi+2i+2yi^2=(3-2y)+(3y+2)i$$

anonymous · Answer

the first part is what math teachers like to call "foil" the second because $i^2=-1$ so $2yi^2=-2y$

anonymous · Answer

and also i separated out the real and imaginary parts
the real part is the part with no $i$ namely $3-2y$ which we can ignore, and the imaginary part is 
$$3y+2$$

anonymous · Answer

since we want this just to be a real number, that means that 
$$3y+2=0$$ and so 
$$y=-\frac{2}{3}$$

itiaax · Answer

Thank you! I'll process the information now :)

anonymous · Answer

k good luck