Question

Help

Answer 1

a) any attempts yet? as a reminder r = sqrt(x^2+y^2) and theta = arctan(y/x)

Answer 2

(17i)/13?

Answer 3

wiat

Answer 4

r = sqrt(13^2+17i^2)

Answer 5

we don't consider the i part (it is assumed that y is graphed in the imaginary plane)

so sqrt(13^2+7^2) and arctan(7/13)

Answer 6

anyway, then you just need to simplify sqrt(13^2 + 7^2) to get sqrt(218) as the modulus

z = __*[cos(theta) + isin(theta)]

where the modulus goes into the blank and the theta value goes into the theta

Answer 7

z = _sqrt 218_*[cos(theta) + isin(theta)]

Answer 8

make sure to also plug in the theta value

Answer 9

1.43 righht

Answer 10

z = _sqrt 218_*[cos(1.43) + isin(1.43)]

Answer 11

arctan(7/13) = ?

Answer 12

z = _sqrt 218_*[cos(28.3) + isin(28.3)]

Answer 13

I would recommend using the radians value here since the other angle is in radians

so 0.49

Answer 14

sqrt 218_*[cos(0.49) + isin(0.49)]

Answer 15

good

then for b and c try to apply the multiplication and division rules of de moivres to your problem

Answer 16

wouldnt it just be

(13 + 7i) * 3(cos(1.43) + isin(1.43)).

Answer 17

notice how the numbers in front of your z and w roots are 3 and sqrt(218) so r1r2 = 3*sqrt(218)

Answer 18

notice also how it calls for theta1 + theta2 so you must add the theta value 0.49 obtained from step a) to 1.43 to obtain the new theta value

Answer 19

0.49+1.43

Answer 20

good so putting everything together what is zw?

Answer 21

1.92

Answer 22

3*sqrt(218)

Answer 23

that's the theta value, but what about the entire expression?

Answer 24

44.29

Answer 25

3*sqrt(218)=44.29

Answer 26

when you replace those values in, what do you get for the entire expression?

Answer 27

3sqrt(218)[cos(1.92)+isin(1.92)]

Answer 28

awesome so that's zw

now repeat the same process for the division formula, be careful because order matters

Answer 29

is theta 1 0.49 or 1.43

Answer 30

it's z/w so theta1 will be the theta value for z (0.49)

Answer 31

(0.20)[cos(-0.94)+isin(-0.94)]

Answer 32

it's z/w so the r-value for z goes in the numerator

sqrt(218)/3 should be the r value not the other way around

Answer 33

(4.9)[cos(-0.94)+isin(-0.94)]

Answer 34

good, so that's it