The expression that represents the value of z is [tex]\sqrt[3]{3 + i\sqrt 3 }[/tex]
Complex numbers are numbers that have real and imaginary parts
A complex number (n) is represented as:
[tex]n = a + bi[/tex]
From the above expression, we have:
Given that:
[tex]z^3 = 3 + \sqrt 3 i[/tex]
Rewrite the above expression as:
[tex]z^3 = 3 + i\sqrt 3[/tex]
Take the cube roots of both sides
[tex]z = \sqrt[3]{3 + i\sqrt 3 }[/tex]
The letters are not given.
Hence, the expression that represents the value of z is [tex]\sqrt[3]{3 + i\sqrt 3 }[/tex]
Read more about complex numbers at:
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