Question

Compute the modulus and argument of each complex number.

Answer 1

r=sqrtx^2+y^2 right

Answer 2

yes

Answer 3

be careful with parentheses

modulus = sqrt(x^2+y^2)

Answer 4

okay so
0

Answer 5

sqrt(x^2+y^2)
sqrt((1)^2+(i)^2) =0

Answer 6

for modulus and theta calculations don't include i, but do include the coefficient

so 1 + i gives us x = 1 and y = 1

Answer 7

sqrt(x^2+y^2)
sqrt((1)^2+(1)^2) =sqrt2

Answer 8

good, keep going

Answer 9

sqrt(x^2+y^2)
sqrt((4)^2+(-4)^2)=4sqrt2


sqrt(x^2+y^2)
sqrt((2)^2+(5)^2)=sqrt29

Answer 10

good

Answer 11

for part IV i kinda forgot how to do iit :/

Answer 12

the argument is just the theta value inside cos and sin

the modulus is the number out in front (2)

Answer 13

okay so modulus = 2

argument = 2pi/3

Answer 14

what about the argument for the other ones,

Answer 15

theta = arctan(y/x).

Answer 16

arctan (5/2)= 68.2 degrees (PartIII)

Answer 17

arctan (4/4) = pi/4 = 45degrees (Part II)

Answer 18

arctan (1/1)=pi/4=45degrees (Part I)

Answer 19

check your sign on part II, it's 4 - 4i so it should be arctan(-4/4)

Answer 20

arctan (-4/4) = -pi/4 = -45degrees (Part II)

Answer 21

good, since we'd usually want a positive theta you can just add 360 degrees (or 2pi) to that

Answer 22

=315 degrees