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How is multiplying  3 - 2i by i2 represented on the complex plane?

 

The complex number 3 - 2i lies in  _____  of the complex plane. When any complex number is multiplied by the imaginary unit, the complex number undergoes a 90° rotation in a counterclockwise direction. This means that the complex product of 3 - 2i and i2 lies in ______ of the complex plane.

 

Fill in the blank options:

quadrant I, quadrant II, quadrant III, quadrant IV

 

 

 

I'm pretty positive I could figure this out if I had it graphed, but I have no idea how to graph this.. if someone could help, I'd appreciate it. I need major help here. I'm struggling really bad:(

 May 14, 2020
 #1
avatar+111360 
+2

(3 - 2i) ( i^2)   =

 

(3 - 2i) (-1)  =

 

-3  +  2i

 

Ignoring the imaginary part  (consider that the y axis  is the imaginary axis), look at the graph here : https://www.desmos.com/calculator/ks69hcjdhx

 

(3, -2i)    lies  in Quad 4

 

So  multiplying this  by  i  rotates it 90° counter-clockwise   and  multiplying this  result  by i   again  rotates it by 90° counter-clockwise  once more....so....we end up in Quad 2  ⇒  (-3 + 2i)  = (-3, 2i)

 

 

cool cool cool 

 May 14, 2020
 #2
avatar+152 
+1

Much appreciation for you omigosh. You have no idea how much that helps. I also tried graphing it on Desmos but I did it wrong and I see where it messed up. Thank you for helping me. Seriously. :)

auxiarc  May 14, 2020
 #3
avatar+111360 
+1

OK.....glad I could help a little .....

 

 

cool cool cool

CPhill  May 14, 2020

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