Answer:
-2.9166
Step-by-step explanation:
Step-by-step explanation:
Shortest way to solve this question is to find the factors of the given expression.
The given expression is (x² + 13).
Now we have to factorize it.
(x² + 13) = x² + (√13)²
= x² + [-(i)²√(13)²] [Since i = √(-1)]
= x² - (i√13)²
= (x - i√3)(x + i√3) [Since (a² - b²) = (a + b)(a - b)]-by-
There are 6 6th roots of 64 To find them, first write 64 in polar form:
64 = 64(cos0 + isin0)
<span>If z = r(cosθ + isinθ) is a 6th root of 64, then z<span>6 </span>= 64</span> By DeMoivre's Theorem, this gives us:
<span>r6[cos(6θ) + isin(6θ)] = 64[cos0 + isin0]</span>
<span>So, r6 = 64 and 6θ = 0° + k(360°)
</span> r = 2 and θ = k(360°)/6 = k(60°), k = 0, 1, 2 ,...
If z is a 6th root of 64, then z = 2[cos(k(60°)) + isin(k(60°))], where k = 0, 1, 2, ...
1st 6th root (set k = 0): 2[cos0° + isin0°] = 2
2nd 6th root (set k = 1): 2[cos60° + isin60°] = 1 + √(3) i
3rd 6th root (set k = 2): 2[cos120° + isin120°] = -1 +√(3) i
4th 6th root (set k = 3): 2[cos180° + isin180°] = -2
5th 6th root (set k = 4): 2[cos240° + isin240°] = -1 - √(3) i
<span>6th 6th root (set k = 5): 2[cos300° +isin300°] = 1 - √(3) i</span>