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SAT Math: Finding an Equivalent Expression Using Complex Numbers 2 Views


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Description:

If , which of the following is equal to the complex number ?


Transcript

00:02

Okay say t shmoop er's If i equals the square

00:05

root of negative one it's A conceptual thing Which of

00:08

the following is equal to the complex Number four plus

00:11

five high over six minus two i this complex number

00:18

is actually a lot more complex iq ated than it

00:21

looks wait that's in the world is anyway The strategy

00:24

here involves conjure gets both the numerator and denominator need

00:28

to be multiplied by the country get of the denominator

00:31

right So the denominators country it looks exactly the same

00:34

as the denominator except the sign for two i switch

00:38

is on ly the sign for the second term changes

00:41

and if you didn't show up for school toe learn

00:43

that this day Well then you're out of luck So

00:46

the sign for six days positive and that negative too

00:49

i becomes positive too I also that fraction more multiplying

00:52

by well doesn't change the overall expressions value because the

00:56

numerator and denominator are the same So we actually multiplied

00:59

by one So that gets us this equation for plus

01:03

five i over six minus two times six plus two

01:06

eye over six plus two i okay were conjugating in

01:10

the denominator The two i terms cancel out Kind of

01:12

like a difference of squares does and there's one real

01:15

term in a nice square term and because i squared

01:17

is negative one and pretty much by definition The denominators

01:21

simplifies to a real term so we just replace each

01:24

ice square term with negative one and then our equation

01:27

goes teo twenty four plus eight i plus thirty i

01:30

plus ten i squared over was that thirty six plus

01:34

twelve i minus twelve i minus four i squared so

01:37

we're just playing across all right and then we just

01:39

combine like terms and it gets us twenty four plus

01:42

thirty eight i minus ten thirty six minus clooney thinkit's

01:48

forty and then the final reduction fourteen plus thirty eight

01:51

i over forty There we go Well this fraction can

01:54

be split into two fractions because the denominator is now

01:57

one term giving us our answer of seven twentieth plus

02:01

nineteen i over twenty it's d well don't split the

02:04

fraction in the question into two different fractions like air

02:08

b did That strategy only works if the denominator is

02:10

one term which is not the case until we multiplied

02:13

by the conjugated So yeah it was a hard problem 00:02:16.08 --> [endTime] if you got it Q does

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