![1. (a) Find real numbers a and b such that a + bi = p.v.(-87]1/3. [4] (b) Consider the following statement. Log(-2)2 = Logza](http://img.homeworklib.com/questions/c23b1040-eaf7-11ea-a63f-fbf6634f2abf.png?x-oss-process=image/resize,w_560)
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1. (a) Find real numbers a and b such that a + bi = p.v.(-87]1/3. [4]...
[4] 1. (a) Find real numbers a and b such that a + bi = p.v.(-87]1/3....
[4] 1. (a) Find real numbers a and b such that a + bi = p.v.(-87]1/3. (b) Consider the following statement. "Log(-2)2 = Logz2 because (-2)2 = 22. Therefore, 2 Log(-2) = 2 Logz." Explain whether or not the statement is true. [4] (c) Consider the following statement. » The rational function (3), where p and q are co-prime non-constant polynomials, is holomorphic everywhere except at the set of zeros of q.” Does this explain if any primitive of (2is...
[4] (a) Find real numbers a and b such that a + bi = p.v.(-87]1/3. (b)...
[4] (a) Find real numbers a and b such that a + bi = p.v.(-87]1/3. (b) Consider the following statement. ”Log(–z)2 = Logz2 because (-2)2 = 22. Therefore, 2 Log(-x) = 2 Logz.” Explain whether or not the statement is true. [4] (c) Consider the following statement. "The rational function P(3), where p and q are co-prime 9(2) non-constant polynomials, is holomorphic everywhere except at the set of zeros of q.” Does this explain if any primitive of P(z) is...
[4] (a) Find real numbers a and b such that a + bi = p.v.(-87]1/3. (b)...
[4] (a) Find real numbers a and b such that a + bi = p.v.(-87]1/3. (b) Consider the following statement. ”Log(–z)2 = Logz2 because (-2)2 = 22. Therefore, 2 Log(-x) = 2 Logz.” Explain whether or not the statement is true. [4] (c) Consider the following statement. "The rational function P(3), where p and q are co-prime 9(2) non-constant polynomials, is holomorphic everywhere except at the set of zeros of q.” Does this explain if any primitive of P(z) is...
solve it ,i need urgent, no need to write neat and clean.. thanks! ......b0nGrr....... 1. (a)...
solve it ,i need urgent, no need to write neat and clean..
thanks!
......b0nGrr.......
1. (a) Find real numbers a and b such that a + bi = p.v.(-86]1/3. [4] (b) Consider the following statement. "Log(-x)2 = Logza because (-2)2 = 22. Therefore, 2 Log(-2) = 2 Logz." Explain whether or not the statement is true. [4] (c) Consider the following statement. "The rational function (2), where p and q are co-prime non-constant polynomials, is holomorphic everywhere except at the...
Q6 (4+3+3+ 6=16 marks) Let Xo, X1, X2 be three distinct real numbers. For polynomials p(x)...
Q6 (4+3+3+ 6=16 marks) Let Xo, X1, X2 be three distinct real numbers. For polynomials p(x) and q(x), define < p(x),q(x) >= p(xo)q(x0) + p(x1)q(x1) + p(x2)q(22). Let p(n) denote the vector space of all polynomials with degree more no than n. (i) Show that < .. > is an inner product in P(2). (ii) Is < ... > an inner product in P(3)? Explain why. (iii) Is <,:> an inner product in P(1)? Explain why. (iv) Consider Xo =...
7.23 Theorem. Let p be a prime congruent to 3 modulo 4. Let a be a natural number with 1 a< p-1. Then a is a quadrut...
7.23 Theorem. Let p be a prime congruent to 3 modulo 4. Let a be a natural number with 1 a< p-1. Then a is a quadrutic residue modulo pif and only ifp-a is a quadratic non-residue modulo p. 7.24 Theorem. Let p be a prime of the form p odd prime. Then p 3 (mod 4). 241 where q is an The next theorem describes the symmetry between primitive roots and quadratic residues for primes arising from odd Sophie...
B. Let p and q be distinct positive prime numbers. Set a p+ (a) Find a...
B. Let p and q be distinct positive prime numbers. Set a p+ (a) Find a monic polynomial f(x) EQlr of degree 4 such that f(a) 0. (b) Explain why part (a) shows that (Q(a):QS4 (c) Note: In order to be sure that IQ(α) : Q-4, we would need to know that f is irreducible. (Do not attempt it, though). Is it enough to show that f(x) has no rational roots? (d) Show V pg E Q(α). Does it follow...
1. Find scalars a,b,c that are real numbers such that at least one of a,b,c is...
1. Find scalars a,b,c that are real numbers such that at least
one of a,b,c is non zero:
2. Find a nonzero vector v in R^4 orthogonal to:
at] +b]+cE]=R] -3
1) If 3iis a zero of p(z)=az2+z3+bz−27, find the real numbers a and b. Enter them...
1) If 3iis a zero of p(z)=az2+z3+bz−27, find the real numbers a and b. Enter them in the form a,b 2) Factorise p(z)=z3−2z2+z−2 into linear factors. Enter them in the format z+3+I, z-6+5*I. 3) Consider p(z)=iz2+z3−2iz−4z2+i+5z−2. Given that z=2−i is a zero of this polynomial, find all of its zeros. Enter them in the form 2+3*I, 4+5*I, 6-7*I
[4] 1. (a) Find real numbers a and b such that a + bi = p.v.(-87]1/3. (b) Consider the following statement. "Log(-2)2 = Logz2 because (-2)2 = 22. Therefore, 2 Log(-2) = 2 Logz." Explain whether or not the statement is true. [4] (c) Consider the following statement. » The rational function (3), where p and q are co-prime non-constant polynomials, is holomorphic everywhere except at the set of zeros of q.” Does this explain if any primitive of (2is...
[4] (a) Find real numbers a and b such that a + bi = p.v.(-87]1/3. (b) Consider the following statement. ”Log(–z)2 = Logz2 because (-2)2 = 22. Therefore, 2 Log(-x) = 2 Logz.” Explain whether or not the statement is true. [4] (c) Consider the following statement. "The rational function P(3), where p and q are co-prime 9(2) non-constant polynomials, is holomorphic everywhere except at the set of zeros of q.” Does this explain if any primitive of P(z) is...
[4] (a) Find real numbers a and b such that a + bi = p.v.(-87]1/3. (b) Consider the following statement. ”Log(–z)2 = Logz2 because (-2)2 = 22. Therefore, 2 Log(-x) = 2 Logz.” Explain whether or not the statement is true. [4] (c) Consider the following statement. "The rational function P(3), where p and q are co-prime 9(2) non-constant polynomials, is holomorphic everywhere except at the set of zeros of q.” Does this explain if any primitive of P(z) is...
solve it ,i need urgent, no need to write neat and clean..
thanks!
......b0nGrr.......
1. (a) Find real numbers a and b such that a + bi = p.v.(-86]1/3. [4] (b) Consider the following statement. "Log(-x)2 = Logza because (-2)2 = 22. Therefore, 2 Log(-2) = 2 Logz." Explain whether or not the statement is true. [4] (c) Consider the following statement. "The rational function (2), where p and q are co-prime non-constant polynomials, is holomorphic everywhere except at the...
Q6 (4+3+3+ 6=16 marks) Let Xo, X1, X2 be three distinct real numbers. For polynomials p(x) and q(x), define < p(x),q(x) >= p(xo)q(x0) + p(x1)q(x1) + p(x2)q(22). Let p(n) denote the vector space of all polynomials with degree more no than n. (i) Show that < .. > is an inner product in P(2). (ii) Is < ... > an inner product in P(3)? Explain why. (iii) Is <,:> an inner product in P(1)? Explain why. (iv) Consider Xo =...
7.23 Theorem. Let p be a prime congruent to 3 modulo 4. Let a be a natural number with 1 a< p-1. Then a is a quadrutic residue modulo pif and only ifp-a is a quadratic non-residue modulo p. 7.24 Theorem. Let p be a prime of the form p odd prime. Then p 3 (mod 4). 241 where q is an The next theorem describes the symmetry between primitive roots and quadratic residues for primes arising from odd Sophie...
B. Let p and q be distinct positive prime numbers. Set a p+ (a) Find a monic polynomial f(x) EQlr of degree 4 such that f(a) 0. (b) Explain why part (a) shows that (Q(a):QS4 (c) Note: In order to be sure that IQ(α) : Q-4, we would need to know that f is irreducible. (Do not attempt it, though). Is it enough to show that f(x) has no rational roots? (d) Show V pg E Q(α). Does it follow...
1. Find scalars a,b,c that are real numbers such that at least
one of a,b,c is non zero:
2. Find a nonzero vector v in R^4 orthogonal to:
at] +b]+cE]=R] -3
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