Question

I need help with complex numbers, can someone please guide me through this prob?

Answer 1

Find the value of k for the quotient \[\frac{ 2 - ki }{ k - i }\]

if it is:

1: A pure imaginary number.

2: A real number.

Answer 2

if \(k\) is purely imaginary, then for a real constant \(b\); \(k=ib\)

Answer 3

\[\frac{2-ki}{k-i}\implies\frac{2-(ib)i}{(bi)-i}\] simplify this

Answer 4

Oh okay, so we're assuming this divides evenly with no remainder?

Answer 5

the quotient is the whole number if times it divides, the remainder is forgotten

Answer 6

i c

Answer 7

Correct and I see that "pure imaginary number" means a complex number with no "real" part. So a complex number is a + bi where a is the real part and bi is imaginary term
So from that you got k = bi

Answer 8

yes

Answer 9

so for starters ... 2 - bi^2 right?

Answer 10

for the numerator: yeah, and use i^2 = -1

Answer 11

\[\frac{ 2 - bi ^{2} }{ i(b-1) }\]

Answer 12

\[\frac{ 2+b }{ i (b-1) }\]

Answer 13

we are supposed to find a value for k, so we need to figure out what b in bi is
let me think about it ...

Answer 14

what do you get if you multiply this by \(\frac ii\)

Answer 15

Hmm something is still missing from the problem ...
I don't think you can solve if you don't know what the fractions equals
It's not an equation and k is supposed to be a number so you can't do long division
k is a number, it's supposed to divide to be another number

Like if you have 24/4 = 6
You have to get the fraction equal to a number
Right now we don't know anything about what the fraction equals so you can't solve

Answer 16

well, I don't think you need the fraction to equal to something in order for it to solve :/

Answer 17

whoever wrote the question just stated it weirdly I reckon

Answer 18

I notice we started from a quotient but it has imaginary terms in it
I think they want me to change that into a + bi form first
So to do that, we can multiply by the conjugate of the bottom ...

\[\frac{ (2 - ki) }{ k-i }\]

Answer 19

I'll try to figure something out
Thanks for your help, @UnkleRhaukus :)

Answer 20

(something about the question isn't making complete sense to me either)

Answer 21

ok so like for this whole time I was talking to myself trying to get this prob to somehow interpret but aye what can u do with a dyslexic person like me merp, ty anyways this prob has got sum issues srsly imma go consult a teacher and he/she shall deal with it cause am going nuts about it ok bye

Answer 22

okbye