10 2. Use De Moivre's theorem to determine 1 in the form a + ib. 2

Q: 6. Find all the roots of the following polynomials: a) p(r) = * - 3.r" +?+ 7x – 30 and b) p (r) = r*…

A: Note: Since we are allowed to solve one question at a time, we have solved the first one. Kindly…

Q: b.) Show that if a and b are positive integers where a is even and b is odd, then (a,b) = (a/2, b).…

A:

Q: (2.1) Determine the conjugate of √5+121+√5-12 √5+121-√5-121

A: Replace i with -i to find the conjugate of a complex number.

Q: The Fibonacci numbers 1, 1, 2, 3, 5, 8, 13.. are defined by the recursion formula xn+1 = Xn + xn-1,…

A:

Q: Use z = a + bi and w = c + di to show that z + w =7 + W.

A: Consider a complex number z=a+bi Then, the complex conjugate of above complex number is given by:…

Q: Suppose that x and y are real numbers such that y is 6 greater than x. What is the smallest possible…

A:

Q: ply DeMorgan's Laws un - && (Ir || a))

A: Introduction: The formula for de morgan's law is given by, ~(a∧b)=~a∨~b~(a∨b)=~a∧~b

Q: 1 1. -to prove that x+y|# | x|+ | y| for all real numbers d) Use x = and y = %3D x and y.

A:

Q: ez = -2

A:

Q: Show that Z₁ Z18. From an abstract algebra, senior level university math course

A: Introduction: The group comprises relatively prime positive integers up to 14 in the range.…

Q: a) Calculate the 4th roots of (5-j3)

A: The objective is to calculate the 4th roots of (5-j 3).

Q: 3) Find integers x and y such that 13x + 15y = 1.

A: We see, 15 - 13 = 2              => k(15 - 13) = 2k for any integer k              => 15 k -…

Q: 5. IS the following statement TRUE or FALSE? If the statement is true, prove it, and it is false,…

A: Introduction: The biggest integer function (also known as the floor function) .:R→Z of a real number…

Q: a) (2+4i)*

A:

Q: 1- Let z,=-5+11i and z3=2-21. Find in the form x+iy a) Re(1/2,) b) 1/ Re (z,) c) z,-z,? d) (z1/z2)

A:

Q: 1. Express in the forrm a + bi. a) (1+ 3i)(1 – i) b) (-3+ i)/(7 – 3i)

A:

Q: A (T+ 7) = A·I+ A ·G A (c.F) = c · (A · T) Verify these two properties by direct computation in the…

A:

Q: a+2b 2 Let W = :a,be R}. Show that -4 lies in W. 2a -1

A:

Q: Find a number z (except 0) such that Az³ + Bz²+ Cz = D 2 1 3 0 -2 -4 00 ^-[ ] ³-R2 :]-[+]-[1] B= 1 2…

A: Solution

Q: 19. Express in a + bi form: (5 – 6yi)(4 + 8i) – [(2 – 3yi) – 3(1+ 6i)]

A:

Q: Prove that V/3 (1-x) (1+2x) 33

A: To Determine :-  ∫01 x13 1- x 231 + 2x  dx  = 2π33