Question

If w is the complex number shown in the figure provided (in comments), which of the following points could be -iw?

Answer 1

Here's the graph

Answer 2

Answer Choices Are A,B,C,D,E

Answer 3

what are they?

Answer 4

look at the picture attached in my first comment to this question

Answer 5

Answer is "A" btw.

Answer 6

d

Answer 7

i is shown, and d is the only point on the -1 plane

Answer 8

Its already negative. So multiplying by negative one rotates it to the first quadrant.

Answer 9

Also, multiplying by -i is the same as dividing by i.

Answer 10

Sorry, please elaborate on "Its already negative. So multiplying by negative one rotates it to the first quadrant."

Answer 11

Well if you were to plot that as a number w would have to be something like -a+bi. Multiplying it by -i makes it. b+ai

Answer 12

\[-\sqrt{-1}=1\] right?

Answer 13

....no lol

Answer 14

or does it equal -1?

Answer 15

\[i=\sqrt{-1}\] right?

Answer 16

yeah.

Answer 17

so what does -i equal?

Answer 18

just the -sqrt(-1) its nothing special as far as I know. Except like:\[e^{\frac{3 \pi}{2}i}\].

Answer 19

yoyo, does that makes more sense? Or are you still stuck?

Answer 20

sorry. im lost on this one

Answer 21

I'm still confused. Could you please start from step 1?

Answer 22

geometrically multiplying by i is the same as rotating the vector 90 degree clockwise. So the answer is a.

Answer 23

Of course. When you have a complex number a+bi. It is interpreted in the complex plane as a point (a,b). So if you are in quadrant 2 you have a negative x and a positive "y" or (-a,b) (assuming a is positive). So, generically, you have (-a,b) or -a+bi. So multiplying by -i gives you. -a(-i)+bi(-i)=ai+(-b)(i^2). Well, i^2=-1 so: ai+(-b)(-1)=b+ai. Which is in the first quadrant. Does that help? :P

Answer 24

The 90 degree rotation is also true. If that helps you.