SOLUTION: choose the quotient 80/ 2-6i in the form a + bi

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Question 1172005: choose the quotient 80/ 2-6i in the form a + bi
Found 2 solutions by Alan3354, Edwin McCravy:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
choose the quotient 80/ 2-6i in the form a + bi
----------------
Choose?
----
80/ 2-6i
40/(1-3i)
Multiply NUM and DEN by the conjugate of the DEN.
40(1+3i)/((1-3i)*(1+3i))
= (40+120i)/10
= 4+12i

Answer by Edwin McCravy(20077) About Me  (Show Source):
You can put this solution on YOUR website!
Here's how to get it using a TI-84 calculator, if you have one.

Set the mode:

Press MODE
Scroll down till you see this:

REAL  a+bi  re^(θi)

The calculator comes from the factory with REAL highlighted.  You want to
change this. 

Press the right arrow key once to highlight "a+bi"
Press ENTER

it will stay highlighted, so leave it that way permanently, as it will
not change anything about the way the calculator functions if you leave
it permanently with "a+bi" highlighted. 

Press 2ND MODE (QUIT)    to get back to the main screen.

Press CLEAR

Here is how to get "i".  It's the middle key on the bottom, the decimal key,
(or the "period" key, if you think of the decimal as a "period".)
But you must press 2ND before you press it.

So type this:

80/(2-6i)    <-- where you get the "i" by pressing 2ND then the decimal key,
                 as explained above 

Press ENTER

You will read 4+12i.

It comes out whole numbers in this case.  But in cases where it comes out with
decimals, press MATH ENTER ENTER and it will change the decimals to fractions.

For instance if you were to have have this problem:

%282%2B7i%29%2F%281%2B3i%29

Type this

(2+7i)/(1+3i)

Press ENTER

Read 2.3+0.1i

Press MATH and ENTER twice, and you will read

23/10+1/10i which is

23%2F10%2Bexpr%281%2F10%29i

Edwin