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Find the solutions $x$ of the equation $$2ix^2+x+3i=0.$$

 Aug 3, 2021
 #1
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The polynomial can be factored:

 

(2x - 3i)(ix - 1) = 0

 

Setting each factor to zero and solving yields the two roots:

 

2x - 3i = 0

2x = 3i

x = 3i/2

 

ix - 1 = 0

ix = 1

x = -i (where we use the fact that 1/i = -i)

 Aug 3, 2021
 #2
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Thank you!

 Aug 3, 2021

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