Question

Please help! I give medals and become a fan!
Convert the following complex number into its polar representation: -4i

a. 16(cos(theta)+ i sin(theta))
b. -4(cos(pi/2) + i sin(pi/2))
c. 4(cos(3pi?2) + i sin(3pi/2))
d. 2(cos(0)+ i sin(0))

Answer 1

But it's negative

Answer 2

yeah i made a mistake didn't i?

Answer 3

Its okay!

Answer 4

so would I graph the solutions and see which one like goes there or?

Answer 5

you need two numbers,
the absolute value (modulus) which should be more or less obvious
what do you think it is?

Answer 6

uhm -4?

Answer 7

i.e. how far is \(-4i\) from the origin \(0+0i\) ?

Answer 8

no
absolute value is a distance just like with real numbers

Answer 9

I'm going to sound really stupid but I have no idea how to solve that

Answer 10

i your head
how many steps is \(-4i\) from \(0\)?

Answer 11

*in your head
sticky keyboard

Answer 12

-4

Answer 13

i don't mean to be annoying, but a distance is never negative
the absolute value is always greater than or equal to zero

Answer 14

no it's fine! I need all the help I can get! So it would just be 4?

Answer 15

yes

Answer 16

you can also always compute
\[|a+bi|=\sqrt{a^2+b^2}\] but if you understand what you are looking for, that would be silly in this case

Answer 17

since \(-4i\) is evidently 4 units down

Answer 18

so the answer would be c. seeing as it's the only one that is a postive 4?

Answer 19

the next number you need is the angle
which also should be more or less clear from the picture

Answer 20

270 degrees