Question

helllllllllllp plsssssss

The complex number z is given by
z = (√3) + i.

Showing your working, express in the form x + iy,
where x and y are real,
(a) iz*/z

Answer 1

@perl

Answer 2

@nincompoop

Answer 3

do you know what z* means or is?

Answer 4

conjugate

Answer 5

@phi

Answer 6

write down what you have so far

Answer 7

first tell me should we multiply like this i(\[\sqrt{3}-i\] )= sqrt3i -i^2

Answer 8

yes, that is correct. however, remember i*i is -1

Answer 9

yes but am stuck.. am not getting the right answer -_-

Answer 10

could solve pls

Answer 11

your not stuck. just not finished.
so fare you have
\[ \frac{i \ z*}{z} = \frac{1+ \sqrt{3} \ i}{\sqrt{3} + i} \]

Answer 12

to get rid of a complex number in the denominator, multiply it by its complex conjugate.
to keep things equal, do the same to the top

Answer 13

i already done all this... am stuck.. i think i have not done it right

Answer 14

let me try again

Answer 15

first, what do you get for
\[ (\sqrt{3} + i)(\sqrt{3} - i)\]?

Answer 16

its the signs problem

Answer 17

do you know FOIL? for multiplying

Answer 18

no

Answer 19

FOIL is a way to remember what to multiply
\[ (\sqrt{3} + i)(\sqrt{3} - i) \]
F irst \( \sqrt{3} \sqrt{3} \)
Outer \( \sqrt{3} \cdot -i \)
Inner \( i \cdot \sqrt{3} \)
Last \( i \cdot -i\)

Answer 20

the other way to remember is use the distributive law

Answer 21

am having a problem with the numerator

Answer 22

First, what do you get for the bottom ?

Answer 23

\[(1+\sqrt{3}i) \times (\sqrt{3}-i)\]

Answer 24

for denominator ive got 4

Answer 25

ok. now the top. You can use FOIL
\[ (1+\sqrt{3}i) (\sqrt{3}-i) \]
First \( 1 \cdot \sqrt{3} \)
Outer \( 1 \cdot -i\)
Inner \( \sqrt{3} i \cdot \sqrt{3} \)
Last \( \sqrt{3} i \cdot -i\)

Answer 26

then what should i get ?

Answer 27

simplify each term. Expect 2 reals (no i) and 2 imag (with an i)
the first two F and O are easy to simplify

Answer 28

sorry ?

Answer 29

yeah i have understood and got

Answer 30

the F (i.e. First) term is 1 * sqr(3) which simplifies to sqr(3)

Answer 31

yes

Answer 32

now simplify the next term (the Outer)

Answer 33

-i

Answer 34

ok, now the Inner term

Answer 35

3i

Answer 36

and the Last

Answer 37

sqrt 3

Answer 38

now add them up and "combine like terms"
\[ \sqrt{3} -i+3i +\sqrt{3} \]

Answer 39

the answer is right now.. thank you so much.. i have another problem

Answer 40

please make it a new post. This one is a bit long.

Answer 41

yes