2. (a) Calculate (i+1)302 + (i − 1)302 and write it in the form of x + iy. (b) Find an upper and lower bound for |z − 2i| if |z − 1| ≤ 1. (c) Find a lower and upper bound for if |z − 1| ≤ 1. -2i

Q: value of ∑n=1∞(6an+9bn) if ∑n=1∞an=8 and ∑n=1∞bn=2.

A:

Q: B. Write the following expressions in sigma notation 1. (2x1-3) + (2x2- 3) + (2x3 – 3) + ... + (2x11…

A:

Q: 13-R] [CLO 3] Simplify the expression a2 b5 c4 / a3(b2)-3d-4 so that each variable appears at most…

A: a2b5c4a3(b2)-3d-4=b5c4a3-2(b2)-3d-4=b5c4a(b2)-3d-4

Q: Form the interpolating polynomial of degree k that satisfies pG) (xo) = f(G) (xo) for 0<j< k.

A: To form: The interpolating polynomial of degree k that satisfies pjx0=fjx0 for 0≤j≤k

Q: Given g(z)- In(8z +z), the derivative g(z) is %3D O 8z + O 9z O 72z +1 7278+1 O 72r +1

A:

Q: (c) (i) Express the decimal 9.999 in the form where a, b € Z.

A:

Q: Find real numbers A, ℎ, and K so that −2x2 + 4x − 8 = A(x − ℎ)2 + k.

A: The quadratic equation is given by -2x2+4x-8 = Ax-h2+k To determine: The values of A, h and k.

Q: Estimate the error in √(x-1)=1+x/2 when |x| &lt; 0.01.

A:

Q: Express the following in the form a + ib (for real a and b): 1 (a) 6+2i (b) (-+ i)¹ (c) i², i³, i4,…

A:

Q: (a) Write down the piecewise form for the function |2x – 3|. (b) Hence or otherwise find all…

A: we have to write the given function in piecewise

Q: Find (x³ + 2x²) dx using the Riemann sum.

A:

Q: Let f(x) = x4 − 9x3 + 23x2 − 15x − 10. Find an integer n1 so that f(x) has a root between x = n1 and…

A:

Q: Q9. (a) (i) Calculate (2 + i√5)(√5 - i). (ii) Hence verify that (√5 - i) is a root of the equ

A: (a) The given expression is 2+i55-i Multiply the terms in the given expression…

Q: Show that Q[x]/⟨x 2 − 2⟩ ≅ Q[x]/⟨x 2 + 4x + 2⟩.

A:

Q: -2 Evaluate the integral (6r +5)°dr.

A: We have to find the given definite integral.

Q: [7 0] Consider A = 5 7 and find AA" and ATA and AA"A or explain why these products do not exist.

A:

Q: 2. [(x – 1) + 5][(x – 1) – 51]. Write the answer in the standard form

A: To write in standard form.

Q: Solve for t in B=Numerator x+y over the denominator t+z

A: The given equation is,

Q: a) [5] Evaluate (2 - 3)² + 6 × (4 + 1) + 3² . B1: b) [5] Determine the polynomial with the…

A: Explanation of the answer is as follows

Q: Multiply (x+ 1) (x – 1) O x² - 1 O x² + 2x + 2 O x² + 1 O x2 - 2x - 1

A:

Q: Express −i+j in the form [a,b]

A: Simplification