2. Which of the following statements are correct? (a) If z = 1+ 0i = x € R, then the definitions of sin z and cos z agree with the usual definitions for real variables. (b) cos z and sin z are 27 periodic. (c) cos² z + sin² z = 1 (d) cos z and sin z are injective functions from C to C

Q: a>0 is constructible, then asqrt(a) is also constructible

A: If a>0 is constructible, then we have to prove that   is also constructible.

Q: -¹ { ₁ 1 (s-1)(s+2)(s+4)) Evaluate L-1

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Q: finding the domain

A: ww will find the domain

Q: 1 (b) 1+j Evaluate (a) 1+j -25 (1+ j2 (3+ j4 2- j5 Show that = 57+j24

A:

Q: Suppose that g:A -> B and f:B -> C where A = B = C = {1, 2, 3, 4}, g ={(1, 4), (2, 1), (3, 1), (4,…

A: Given:-   Suppose that g:A -> B and f:B -> C where A = B = C = {1, 2, 3, 4}, g ={(1, 4), (2,…

Q: Let det(A) = 5 and det(A + B) = 20. We conclude that det(1+A¬²B) = 15

A: Given: |A|=5|A+B|=20True/False|I+A−1B|=15

Q: Vx, A(x) → B(x) 3x, A(x) ^ C(x) Vx, C(x) → D(x) ..3x, B(x) A D(x)

A:

Q: what Is the conjugate of Js -J2i ? a. Jo -Joi d. -i b.Ja -ぶ

A:

Q: Use a system of equations to write the partial fraction decomposition of the rational expression.…

A: The objective is to find the partial fractions for the given equation

Q: Evaluate (1 + i)(¹ - i). (1

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Q: Evaluate (xD)(xD)(xD){x² + 2ez} which can be written (xD)3{x2 + 2e*}. (b) Is this the same as…

A:

Q: 5 (z-1)(x+4) (shape +

A: NOTE: Refresh your page if you can't see any equations. . use the partial fraction…

Q: f5(x³ + x)⁹ (3x² + 1)dx O 5(x³+x) ¹0+C 10 (x²³+x) ¹0 10 +C O 45(x³ + x) +C O(x³ + x)¹0+C

A:

Q: Evaluate: (2) A5₁ Clearly showing your working

A: We need to evaluate i. The meaning of a5(2) is the present value of an immediate annuity of an…

Q: ( ii) μ ((2, 5](3, 6))

A:

Q: 2. Find Argz and argz (a) (1-6)* (b) ivs (e) 금

A: (a) Here 1 - i4 = (1 - 1 - 2i)2             = -2i2             = -4So  Arg(z) = π - tan-10-4 = π -…

Q: If f(x) = .Determine the value of E) (d) 8 (e) None (a)

A: Use the formula for  summation of infinity geometric series.

Q: If x>-I show Hhat Cl+x)> \+nx ,H

A:

Q: 1. Evaluate the line integral f x² dx + y²dy + z²dz, where C consists of the line segment from…

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Q: If f(z) = ev8=rl then the simplify form of f(z) is: A) f(z) = ie-2vz B) f(z) = -i e?v2 C) f(z) =…

A: Given function is fz=e8−πi. We have to find the simplify form of fz. We know that eix=cosx+isinx…

Q: lhecocfficient al xinthelbinomial.cxpansion «drC2 – Bei) iis -1000 :B 1080 C 360 D 360

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Q: Show that f(x) = 3x - 5 is a bijection.

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Q: (c) SO YOUR TURN 3 [(ar²+ Find (6x² + 8x-9) dx. b R. Exam the de

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Q: 1. 1(a-e) Evaluate the following. (a) (b) |(3 + 3i)50| (c) (V3+i)

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Q: 교고 + z-2 I+ -2, b) f(x) = I+2 -3, I = -2;

A:

Q: (²)

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Q: "((71) = (71)) 11A (9)

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Q: 1337 i+1` Compute ()

A:

Q: Prove by contraposition that if x^5 + 7x^3 + 5x >= x^4 + x^2 +8, then x >= 0

A: Proof using contraposition: If we want to prove "if A, then B", then using contrapositive statement…

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A:

Q: Simplify. 18-2² (3+8)+2(2)

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Q: g) (f + g)(7)

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Q: Proof that: 12-a) =r → そ= a+re

A: The solution is:

Q: 36 7(modulo3)

A: Concept Used: Consider  a≡b (modulo n) means n/(a-b)i.e. a-b=kn,          for n=integer⇒a=b+kn

Q: Discrete Math Show that f(x) = 3x - 5 is a bijection

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Q: (-7, 10,-3) and r (1) = (1- 41, 6t- 5, 1- 5)

A:

Q: I llustrate with. the help oD examples? the yeflection principle

A: The principle of reflection is that when a ray of light is reflected from a smooth surface the angle…