Question

Simple differential equation problem but I'm a bit confused

Answer 1

Express the complex number -7i in the following form:

\[R(\cos(\theta)+i\sin(\theta))=R e^{i\theta}\]\[R >0, 0\le\theta \le2\pi\]

Answer 2

Now I understand that we can find R by using the form a+bi and
\[R=\sqrt{a^2+b^2}\]
but I don't understand the logic behind finding the exact angle =/

Answer 3

for -7i?

Answer 4

this puts on the y-axis
which means theta is either pi/2 or 3pi/2 since you put theta between 0 and 2pi
choosing whether it be pi/2 or 3pi/2 is based on how you also chose r

Answer 5

it seems you are choosing r to be positive so you should use 3pi/2 \[7(\cos(\frac{3\pi}{2})+i \sin(\frac{3\pi}{2}))\]

Answer 6

Hmm, I'm still a bit confused -- what do you mean by it's put on the y-axis? Maybe it'd help if I was ever taught how to graph imaginary functions? >_<''

Answer 7

do you know how to plot -7i?

Answer 8

oh you don't know to plot those...

Answer 9

the y-axis is the imaginary axis
the x-axis is the real axis

Answer 10

when plotting a+bi
think about plotting (a,b)

Answer 11

Ahh that makes sense. -7 is below the x-axis on the y-axis and this corresponds to the 3pi/2 angle

Answer 12

also...