Question

Let z_1=2+3i and z_2=1-i. Perform the indicated operations and write the solutions in the form a + b i.
z_1/z_2= ?

Answer 1

a. 5/2+5/2i
b. -1/2+5/2i
c. 1/2+5/2i
d. -5/2+5/2i

Answer 2

To do this, multiply top and bottom by the complex conjugate of z_2

the complex conjugate of z_2 is z_2 with its imaginary part negated:
1-(-i)= 1+i

so you need to be able to multiply 2 complex numbers to finish the problem. do you know how to do that?

Answer 3

I don't :(

Answer 4

do you know how to multiply (a+b)(c+d) (using FOIL)?

Answer 5

Oh, yes.

Answer 6

what do you get for (a+b)(c+d) ?

Answer 7

ac+ad+bc+bd

Answer 8

OK. use the exact same idea for (1+i)(1-i)

Answer 9

2?

Answer 10

1-i+i-i^2
but i^2= -1 , so
1 - (-1)= 2

that is the denominator of your problem
now do
(2+3i)(1+i)

Answer 11

-1+5i

Answer 12

that is the top, so your answer is
\[ \frac{-1+5i}{2} \]
this is the same as
\[ \frac{-1}{2} + \frac{5}{2} i \]

Answer 13

So, to summarize, to do division, multiply top and bottom by the complex conjugate of the bottom number.

Answer 14

Thanks phi! I really appreciate your help!