Question

Simplify the given expression: (6 + 2i) − (8 − 3i)

Answer 1

the minus sign out front in
- (8 -3i)
means -1*(8 - 3i)
distribute the -1 ... which means multiply each term inside the parens by -1
then combine "like terms" (add up the reals, and add up the imaginaries)

Answer 2

-8+3i

Answer 3

yes, now you have
6 + 2i -8 +3i

combine "like terms"

Answer 4

in other words,
(6-8) + (2i + 3i)

Answer 5

-2+5i

Answer 6

yes

Answer 7

ok that was given

Answer 8

wt about this

Answer 9

Simplify the given expression:

(−5 + 3i) • (1 − 2i)

Answer 10

do you know FOIL? or in general , how to multiply for example
(x+y)(a+b)
?

Answer 11

-5+6i

Answer 12

sry that was the wrong question to ask

Answer 13

-5-6i

Answer 14

?
what is the question?

Answer 15

This is it
Simplify the given expression:

4 divided by the quantity of 3 minus 2i

Answer 16

\[ \frac{4}{3-2i} \]
multiply top and bottom by 3+2i
can you do that?

Answer 17

12-8i

Answer 18

what did you get for (3-2i)(3+2i) ? (the bottom part)

Answer 19

the top part is 4(3+2i) = 12+8i

we need the bottom part (3-2i)(3+2i)

Answer 20

12+8i top,
13 bottom

Answer 21

so the answer is
\[ \frac{12}{13} + \frac{8}{13} i \]

not very pretty or simple, but at least it is in standard a+ bi form

Answer 22

Next question

Answer 23

Simplify the given expression:

(4 + 2i) − (1 − 7i)

Answer 24

same idea as the one at the top. can you do it?

Answer 25

oh, nvm i got it

Answer 26

thx

Answer 27

another one

Answer 28

(−5 + 3i) • (1 − 2i)

Answer 29

i messed up on it i think

Answer 30

do you know FOIL?

Answer 31

i got 5i-6

Answer 32

-5-6i

Answer 33

how?

Answer 34

you can use the distributive Law or FOIL (same thing, but a way to remember it)

Answer 35

Are you asking how I got it wrong or how I got to this answer?

Answer 36

how did you get that answer? what steps did you do?

Answer 37

i did the foil method, so i got -6isquared + 5 -5

Answer 38

but it has to be simplified

Answer 39

here is using the distributive law: A (x+y) = Ax + A y
(−5 + 3i) • (1 − 2i)

in this case, A is (-5 + 3i), and we write
(-5 + 3i)* 1 + (-5 + 3i)(-2i)

now use the distributive property a second time (twice)
the first part 1*(-5 + 3i) is easy : -5 + 3i
the 2nd part: -2i*(-5) + (3i)*(-2i) = +10i -6i^2

so we get
-5 + 3i +10i -6i^2

which should match the terms you get if you use FOIL

next, remember i^2 or i*i is -1 <--- IMPORTANT SIMPLIFICATION

in other words, we have
-5 + 3i +10i -6*-1

Answer 40

now simplify and combine like terms

Answer 41

oh ok, thx

Answer 42

what is an extraneous soulution

Answer 43

https://en.wikipedia.org/wiki/Extraneous_and_missing_solutions

Answer 44

oh ok, so here's the question

Answer 45

4Square root of x minus 3 = 12, solve for x and identify if it is an extraneous solution

Answer 46

is it not extranuous

Answer 47

x = 0

Answer 48

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