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By using the De Moivre's formula, the <em>quartic</em> roots of the <em>complex</em> numbers (in <em>polar</em> form) are z₁ = (√2, π/6), z₂ = (√2, 2π/3), z₃ = (√2, 7π/6), z₄ = (√2, 5π/3).
<h3>How to find the roots of a complex number</h3>
<em>Complex</em> numbers are numbers of the form a + i b, where a and b are the <em>real</em> and <em>imaginary</em> component, respectively. In other words, <em>complex</em> numbers are an expansion from <em>real</em> numbers. The n-th root of a <em>complex</em> number is found by using the De Moivre's formula:
, for i = {0, 1, 2, ..., n - 1}.
Where:
- r - Norm of the complex number.
- θ - Direction of the complex number, in radians.
The norm of the <em>complex</em> number is found by Pythagorean theorem:
r = 4
And the direction is determined below:
θ = 2π/3 rad
Then, the <em>quartic</em> roots of the <em>complex</em> numbers (in <em>polar</em> form) are z₁ = (√2, π/6), z₂ = (√2, 2π/3), z₃ = (√2, 7π/6), z₄ = (√2, 5π/3).
To learn more on complex numbers: brainly.com/question/10251853
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