Considet the quadratic integer ring Z[sqrt{D}] where D is a square free integer (a) Show 3 is reducible in D = -2 yet irreducible in D = -5 and (b) is 3 prime when D is -2 and -5? Justify!   please do not provide solution in image format thank you!

owid%3D1168028#3question3 Magni fier Highlight mode Review later 3. State the product of x + yi and its conjugate in simplest a + bi form.

X SMATH 1115 520Complex%20Numbers.pdf 1/1 | O a. √-5 b. 2+3i c. 1 d. √18 7. C. may apply. 2. Identify the number as real, complex, pure imaginary, or nonreal complex. More than one of these descriptions 3. Write the number as the product of a real number and i. a. √-144 b. √-45 C. √-8 d. √-23 d. X 4. Multiply of divide radicals with negative radicands. a. √-4 √-4 √-12 b. -45 1 -25-√-6 √5 MATH 1115 100% a. + 18 5. Write the number in standard form a + bi. -8+√-12 16 F7 6. Find the sum or difference. Write the answer in standard form. a. (-3+4i) - (4 - 5i) + (9 + i) b. (7-3i) (3 + 3i) Find the product. Write the answer in standard form. a. (-4+2i)² b. (4+7i)(-2-5i) c. (6+8i)(6 - 8i) d. (3+5i) ² (7-3i) 8. Find the quotient. Write the answer in standard form. 3+4i 3-41 8 F8 X 9 F9 + V F10 F11 F12 + 11 Delete 40 0 Ō 12:20 PM 8/31/2022

Use DeMoivre's Theorem to find the following. Write your answer in standard form. 3 (-4 - 41) O- 128 7 128 - 1281 O - 128 - 1281 128 + 1281 - 128 + 128i

Bank of America New Tab 7- Factoring Polynomials (GCFS) ☆ D O Last edit was 1 hour ago 12 +. BIUA 1. Which expression represents 36r² – 100y° factored completely? 1) 2(9x+25y')(9, 25y') 2) 4(3x + 5y')(3x- 5y') 3) (6x+ 10y)(6x – 10y') 4) (18x+50y’)(18x – 50y')

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16. Use the properties of the dot product to simplify each of the following expressions.