Final answer:
To find all the values of the given expression, we first simplify each component and then multiply them. Using the quadratic formula, we can determine the possible values of x in the equation ax^2 + bx + c = 0. Substituting the given values, we find that x can be 5/6 or -3/2.
Step-by-step explanation:
To find all the values of the expression (1 + 3 – √i)^13 * (1 + 3i)^13, we can simplify the expressions individually and then multiply them.
First, let's simplify (1 + 3 – √i)^13:
Using the given equation (I₁ = 1₂ + 13 = (6 − 21 ₁) + (22.5 — 31 ₁) = 28.5 — 51 ₁), we can substitute the values a=3, b=13, and c=-10 into the quadratic formula. This will give us the values of x in the equation ax^2 + bx + c = 0.
Using the quadratic formula, we get x = (-b ± √(b^2 - 4ac))/(2a). Substituting the given values, we get x = (-13 ± √(13^2 - 4*3*(-10)))/(2*3). Simplifying further, we get x = (-13 ± √169 + 120)/6. This gives us two possible values for x: (-13 + √289)/6 and (-13 - √289)/6. These simplify to 5/6 and -3/2 respectively.