The solution of the equation [tex]x^2[/tex] + 27 = 0 when solved over the complex number is [tex]\sqrt{27}i[/tex]
The equation is
[tex]x^2[/tex] + 27 = 0
The complex number is the combination of a real number and an imaginary number.
Here we have to solve the equation and find the value of x
[tex]x^2[/tex] + 27 = 0
Subtract 27 from the both side of the equation
[tex]x^2[/tex] + 27 - 27= -27
[tex]x^2[/tex] = -27
Take square root on the both side of the equation
x = [tex]\sqrt{-27}[/tex]
We know,
[tex]\sqrt{-1}[/tex] = i
The substitute this value in the equation
Then the value of x = [tex]\sqrt{27}i[/tex]
Hence, the solution of the equation [tex]x^2[/tex] + 27 = 0 when solved over the complex number is [tex]\sqrt{27}i[/tex]
Learn more about complex number here
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