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The complex number  −2+4i 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 _____ direction. This means that the complex product of  −2+4i and  i^3 lies in _______ of the complex plane.

 

choices = clockwise, quadrant II, quadrant I, quadrant IV, quadrant III, counterclockwise

 

thanks guys!

 Apr 30, 2020
 #1
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Quadrant II

 

(-2 + 4i) * i^3  =    -2i^3  + 4i^4   =  -2 (-i) + 4  =   4 + 2i

 

So....multiplying by i^3  results in a 90° clockwise rotation

 

So the resulting product lies in Quadrant 1

 

cool cool cool

 Apr 30, 2020

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