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avatar+416 

Find all complex numbers z such that z^4 = -4.

Note: All solutions should be expressed in the form a+bi, where a and b are real numbers.

 

So i know that z^4 = -4. I also know that z is a complex number. I dont really know what to do now! Can someone help a little pls!

 Apr 22, 2020
 #1
avatar+23518 
+1

DO a search for this Q and answer.....it has been posted multiple times in recent months....

 Apr 22, 2020
edited by ElectricPavlov  Apr 22, 2020
 #2
avatar+416 
+1

May you please post a link since I didnt see any?

 Apr 22, 2020
 #3
avatar+23518 
0

I can't finsd it either....as I recall it was   +-1 +- i      (four solutions)

ElectricPavlov  Apr 22, 2020
 #4
avatar+20767 
0

Write -4  into r·( cos(theta) + i·sin(theta) ) form   =   4( cos(180o) + i·sin(180o) )

 

Find one fourth root:  41/4 ( cos( 180o / 4 ) + i·sin( 180o / 4) )  =  1 + i

 

The other three roots are each a 90o rotation from the previous root:  -1 + i, -1 - i, i - i

 Apr 22, 2020

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