Question

Write each complex number in rectangular form. Plot and label (with a - d) each point on the polar axes below.

Answer 1

let's use a) as an example

2(cos(135) + isin(135))

you basically just need to distribute the 2 to get 2cos(135) + 2i*sin(135), then replace cos(135) and sin(135) with their actual values (use a calculator)

Answer 2

2(cos(135) + isin(135))

= -1 + I sqrt 2

Answer 3

= -1 + i sqrt 2 *****

Answer 4

wait

Answer 5

hm

2*cos(135) = -2/sqrt(2)

so -2/sqrt(2) + sqrt(2) * i
should do it

Answer 6

(the coefficient sqrt(2) is written before the i)

Answer 7

i AM still getting the same answer

Answer 8

parentheses are important

-1 + i sqrt 2 is not the same as [-1 + i]sqrt(2)

Answer 9

the one on top is the one written in standard form

Answer 10

Okay so it needs to include parentheses making the answer [-1 + i]sqrt(2)

Answer 11

solve that i get -1.41

Answer 12

you do not need to do anything with the coordinates once you have them

-2/sqrt(2) + sqrt(2) * i is sufficient, nothing else needs to be done

Answer 13

similar thought process for b)

Answer 14

3cos(120) + 3i*sin(120),

3*cos(120)=-3/sqrt3

Answer 15

i think ;O

Answer 16

cos(120) = -1/2 so 3cos(120) = -3/2

don't forget about the 3*i*sin(120)

Answer 17

-3/2

3isqrt3/2

Answer 18

good so -3/2 + [3*sqrt(3)/2]i is your solution

Answer 19

cos(5pi/4) = -1/sqrt2 so 5cos(5pi/4) = -5/2

5*i*sin(5pi/4) = -5i/sqrt2

Answer 20

almost

5cos(5pi/4) = -5/sqrt(2)

so your sol'n is -5/sqrt(2) + [-5/sqrt(2)]i

Answer 21

any attempts on d yet?

Answer 22

cos(5pi/3) = 1/2 so 4cos(5pi/3) = 2

4*i*sin(5pi/3) = -2i/sqrt3

Answer 23

good so 2 - (-2/sqrt(3))i

Answer 24

wait isn't it just -2sqrt(3) i

Answer 25

okay so c is cos(5pi/4) = -1/sqrt2 so 5cos(5pi/4) = -5/2

5*i*sin(5pi/4) = -5i/sqrt2

and d is

cos(5pi/3) = 1/2 so 4cos(5pi/3) = 2

4*i*sin(5pi/3) = -2i/sqrt3i

Answer 26

you need to combine the values to get the complete coordinate

c: -5/sqrt(2) + [-5/sqrt(2)]i
d: 2 - 2sqrt(3) * i

Answer 27

those are your solutions