divide and simplify [1-i][/2+i] to the form of a+bi

[alcalet]

divide and simplify to the form of a+bi
[1-i][/2+i]

 

[stapel]

divide and simplify to the form of a+bi
[1-i][/2+i]

What is the meaning of the brackets in the above? By what are you supposed to divide the above? What is the meaning of the initial "slash" character inside the second set of brackets?

How far have you gotten? Where are you stuck?

Please be complete. Thank you!

Eliz.

 

[alcalet]

1-i divided by 2+i I am copletely stuck I dont even know where to begin.

 

[pka]

Try this: \(\displaystyle \frac{{1 - i}}{{2 + i}} \cdot \frac{{2 - i}}{{2 - i}}\).

 

[alcalet]

then do i foil or what do i do

 

[pka]

then do i foil or what do i do

Just multiple out the numerators and denominators.

 

[alcalet]

that would give me 2+1i+2i-i^2/4-i^2

 

[pka]

\(\displaystyle i^2 = - 1\quad \Rightarrow \quad \frac{{1 - i}}{{2 + i}} \cdot \frac{{2 - i}}{{2 - i}} = \frac{{2 - 3i + i^2 }}{{4 - i^2 }} = \frac{{1 - 3i}}{5}\)