Question

+5i?

Answer 1

a: +5i would be the conjugate not the modulus/argument

modulus is the length (or the r value)
argument is the angle

so as usual r = sqrt(x^2 + y^2) and angle = arctan(y/x)

for a) we only have a y-value (-5) so we have to do a quick sketch to find the angle:

Answer 2

I believe that's treating i as an independent variable not the imaginary value i

Answer 3

parabola

Answer 4

hm? it's not asking for a shape it's asking for a modulus and argument

Answer 5

im not sure actually :/

Answer 6

-5i (in other words, 0 - 5i) means that x = 0 and y = -5

calculate r = sqrt(x^2 + y^2) and find the angle:

Answer 7

notice how the angle is made of three 90 degree angles

3*90 gives the argument

r = sqrt(0^2 + (-5)^2) gives the modulus

Answer 8

5

Answer 9

so argument = 3*90 = 270
Modulus= r = sqrt(0^2 + (-5)^2) = 5

Answer 10

good

Answer 11

anyway for b) the number in front (sqrt(10)) is the modulus, and the angle of cos and sin is the argument

Answer 12

Wait the number in front of sqrt 10?

Answer 13

sqrt(10) is the modulus

Answer 14

oh okay

so

modulus= sqrt 10

argument = arccos (sqrt 10) = 1.18

arcsin (sqrt 10) = 1.57

Answer 15

like that

Answer 16

if you look at the original equation the argument is just the angle that is contained within the cos and sin expressions

since its cos(5pi/7) and sin(5pi/7) the argument is just 5pi/7

Answer 17

oh right because we are finding both cos and sin and 5pi/7 is given