Question

Find the quotient of the complex numbers. Express your answer in trigonometric form.
z1= 5(cos25Deg + i sin25Deg)
z2= 2(cos80Deg + isin80Deg)

Answer 1

Explain, please? (:

Answer 2

when we divide complex numbers , we
1) divide the magnitude
2) subtract the angles.

Answer 3

so, we need z1/z2 here, right ?
what u get resultant magnitude after dividing the magnitudes of z1 and z2 ?

Answer 4

so 5/2?

Answer 5

yup, u got the magnitude as 5/2
now subtract the angles, 25-80 = ... ?

Answer 6

-55 ? :o

Answer 7

yes, to make it positive we can add or subtract 360 degrees, what do we do, add or subtract ?

Answer 8

add.. :)

Answer 9

correct, -55+360 = ... ?

Answer 10

305 !

Answer 11

you got it! :)

Answer 12

Thanks you ! :D <3

Answer 13

mind helping me with a few others? ^~^

Answer 14

most welcome ^_^
i will be glad to :)

Answer 15

OK, how do you simplify (2-3i)+ (5-6i) ? :)

Answer 16

just addition of complex numbers., oh thats simple ,
add up "non-i" terms called real part, and "the i" part, called imaginary part

like fo ex : (a+bi) - (c-di) = a-c + (b+d)i

Answer 17

so 7+ -9i ?

Answer 18

7-9i
yup, absolutely correct! :D

Answer 19

yay (: okay, and i is -1 right?

Answer 20

or is correct just like that? .__.

Answer 21

actually , its "square root" of -1
\(\large \color{green}{i=\sqrt{-1}}\)

Answer 22

ohhh okay (: !

Answer 23

got it !

Answer 24

Find the product of the complex numbers. Express your answer in trigonometric form.
z1= 7(cos 15Deg + i sin 15Deg)
z2=2(cos 110Deg+ i sin 110Deg) ...? :o

Answer 25

when we multiply complex numbers , we
1) multiply the magnitude
2) add the angles.
give it a shot!

Answer 26

so 14, 125 and 125 :D

Answer 27

14(cos 125Deg +i sin 125 Deg)

Answer 28

\(\huge \color{red}\checkmark\)

Answer 29

:D <3

Answer 30

okay

Answer 31

\[z1=5\left( \cos 25+\iota \sin 25 \right)=5 e ^{25\iota} \]
\[z2=2\left( \cos 80+\iota \sin 80 \right)=2 e ^{80 \iota} \]
\[\frac{ z1 }{z2 }=\frac{ 5e ^{25 \iota} }{2 e ^{80 \iota} }=\frac{ 5 }{2 }e ^{25 \iota-80 \iota}=\frac{ 5 }{2 } e ^{-55 \iota} =\frac{ 5 }{ 2 }e ^{\iota \left( -55+360 \right)}=\frac{ 5 }{2 }e ^{305 \iota} =\frac{ 5 }{2 } \left( \cos 305+\iota \sin 305 \right) \] \]

Answer 32

Find the product of the complex numbers. Express your answer in trigonometric form.

Answer 33

?

Answer 34

Do we multiply the magnitude here too ?.. :o

Answer 35

yup, try ?

Answer 36

so.... 12

Answer 37

yes and
\(\pi/3+2\pi/5 =...?\)

Answer 38

\[11\pi/15\]

Answer 39

?

Answer 40

D: idk

Answer 41

yup, correct :)

Answer 42

yay! (:

Answer 43

When it asks what is the conjugate of 5+2i what does that mean?

Answer 44

conjugate of \(\large a+bi\) is simply \(\large a-bi\)
like conjugate of 3-4i will be 3+4i :)

Answer 45

so.. 5-2i ?? :D

Answer 46

the opposite (: !

Answer 47

yes! you learn fast :D

Answer 48

yay ! :D yeah, I just need a little push sometimes from nice and smart strangers like you x__x

Answer 49

:D

Answer 50

Find the quotient of z1 by z2. Express your answer in trigonometric form.

Answer 51

So.... you multiply !! :D RIght? :)

Answer 52

quotient means dividing...
and what do we do to divide complex numbers ?

Answer 53

3/7 ...

Answer 54

:o and i'm not sure. .. .__. :o Lol

Answer 55

my very first comment!
when we divide complex numbers , we
1) divide the magnitude
2) subtract the angles.

so 3/7 is correct
what about the angle ?

Answer 56

RIIIGHHHT. so \[-\pi/8\] ?

Answer 57

yup!
is that in any of the choices ?

Answer 58

mhm (: