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 Jul 25, 2021
 #1
avatar+2193 
+2

z^7 + 8z^4 - 2iz^3 - 16i = 0

z^4(z^3 + 8) - 2i(z^3 + 8) = 0

(z^4 - 2i)(z^3 + 8) = 0 

So... (z^4 - 2i) = 0 or (z^3 + 8) = 0

Remember to thank the past answerers to your questions. :))

 

=^._.^=

 Jul 25, 2021
 #2
avatar+24 
+3

Wait im kind of confused on how you went from this z^4(z^3 + 8) - 2i(z^3 + 8) = 0 to this (z^4 - 2i)(z^3 + 8) = 0. The answer is prob correct tho.

Tr1ck3d  Jul 26, 2021
 #3
avatar+114462 
+2

Thanks catmg  laugh

 

Hi Tr1

 

Think about this

3x + 5x  = 8x because you started with 3x and you added another 5x.  so you have (3+5)x

 

ctmeg had

z^4(z^3 + 8) - 2i(z^3 + 8) = 0

 

Here you have  z^4 lots of (x^3+8)  and from that you are taking away  2i lots of (z^3+8)

so you end up with

 

\((z^4-2i) \;\;lots\;\; of \;\;(z^3+8) = (z^4-2i) ( z^3+8) \)

 

Think about it.   laugh

Melody  Jul 26, 2021

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