) ( 7+8i 4+5i 6–3i 8-4i Problem 4: Evaluate

Q: Question 5: If a = ~q and KB = (p (q v r) ^~p, prove using the analysis method (proof based on…

A: We know

Q: Find the two smallest positive solutions of 5sin(5x)=3

A: 5sin(5x)=3 sin(5x)=.6 sin(5x)=sin36.87°

Q: Question 18 -미ch2e-coth2e|+C csch2zdz = A) True B) False

A: A detailed solution is given below

Q: 13.8 in. 10.1 in.

A: Given that radius is 10.1 in and height is 13.8 in. The objective is to find the total surface area…

Q: (1+i)·(10260°) (3–7i)+(9/120°) . Express your answer in rectangular form.

A:

Q: Problem 5. Using the definitions for O and N, prove formally that a) n³+15n+2 is O(nª) b) 2n³ +25n…

A:

Q: Perform the computations in the given question and express the results in standard form a+ bi.…

A: 4-3i4+3iRationalise the…

Q: Perform the computations in the given question and express the results in standard form a+ bi.   i(2…

A: Given i(2 + i)2

Q: 1 ( Problem 30. Prove that PP1)

A: As per our guidelines we are supposed to solve only one question. For the question (30), the…

Q: QUESTION 10 Suppose In(a) =2, In(b) = 5, and In(c) = 3. Evaluate the statement: In(c QUESTION 11…

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Q: 6 - 2 Compute A - 513 and (5I3 )A, where A = - 5 4 - 7 2 2 A- 513 (513)A = O 3. 4)

A:

Q: Suppose z = 7+-8i and w = 9+7i. Then Re (2)=? %3D

A:

Q: Show that: In(-1+/3i) = In2 + 2 ( n + Ti, where n = 0, ±1, ±2, ±3.... 3

A: Show that    ln-1+3i=ln 2+2n+13πi.

Q: How many integer solutions are there to the equation x1+x2+x3+ x4 25 subject to x; > i? Let y. X,-\,…

A:

Q: If A = -2 - 3i, and B = 3 + 4i, what is AB?

A:

Q: Use the method of difference tables to find a closed formula in terms of n for the > (8i + 5) i=1

A: This is the question of counting and discrete math.

Q: Fill in each blank so that the resulting statement is true.

A: Given:∑(5i+3)i=117 To find: The first three terms of∑(5i+3)i=117 and their common difference.

Q: Compute: 19 (4-2i)(4+2i)

A:

Q: Problem 19.1. Prove that 2019 can not be represented as a sum of three fourth powers o integers…

A: Take the fourth power of integers from 1 to 7 and obtain that 74 is greater than 2019. Therefore, to…

Q: Solve the problem. 14) If u = -9i – 2j and v = -3i + 7j, find u V.

A: Let us consider two vectors u=ai+bj and v=ci+dj then u-v=(a-c)i + (b-d)j

Q: 1. Given that z1 = 3 + i, z2 = 4 – 3i, z3 = -1+ 2i and z4 = -2 – 5i, find 21+z2 Z3Z4

A:

Q: Problem 3: Prove (directly from the definition) that for any odd integers a and b, a? +3b is even

A: Set theory: number system properties of integers

Q: write out the first few lines of Pascal's triangle and then use it to expand (3x+2y)^4

A: To write: First few lines of pascals triangle and then use it to expand 3x+2y4. Calculation:…

Q: Problem 3. Let a be an integer that is coprime with 240. Prove that 240|a4 – 1. -

A:

Q: Consider the Kenken Puzzle * 6+ 12x 3 4+ 4x y 2+ 3 1 What should be the value of x? O 1 3-

A:

Q: 27 1+1 Evaluate the expression (2i – 1)² Express the answer in rectangular form. 1+i,

A: The rectangular form of a complex number is z=x+iy. The conjugate of the complex number: z=x+iy is…

Q: 1- Find the following: а) i(2 — 3i)(3 + 5i) b) i/(i – 1) с) (1 + i)30

A: Given that: a)i(2-3i)(3+5i)b)ii-1c)(1+i)30

Q: 1+ 2i = a + bi , then z = 3- 4i 2 34. If z- 1 z ==+= B 2 Z=- 5 D -152I52N In N

A:

Q: Reduce Z= (1-2i) (3+2i), to the form a + ib а. 7+4i b. other С. 7-2i d. 7-4i O e. 4-4i

A: We will find out the required value.

Q: 14. Find all solutions to 2sin(5x)-3V3 =-4/3. State exact values only. %3D

A: Given equation, 2sin5x-33=-43

Q: QUESTION 16 Sum of two numbers is 67, and their difference is 29. Find the numbers. O 1.40 and 20…

A:

Q: Problem 3: Find two integers x and y that satisfy the equation 388x + 244y = 4 Problem 4: Solve the…

A:

Q: In problems where z1, z2, Z3 are given, use the following values. = 2 – 10i, z2 = 1 – 5i, z3 = 10 –…

A: Given that z1=2-10iz2=1-5iz3=10-2i To calculate z1z2z3 we use the normal multiplication of complex…

Q: Evaluate, N = (3+4i)(1+2i) %3D -0.9382 + 0.6342i

A: Here we have, N=3+4i1+2i taking log both sides,

Q: 3 If A = 1] show that A² - 5A + 7I = 0. %3D %3D -1 2

A:

Q: Problem 3. Let a be an integer that is coprime with 240. Prove that 240|a4 – 1.

A: Fermat's Little Theorem: Let p be a prime which does not divide the integer a, then ap-1 ≡ 1 (mod…

Q: Problem 2: Given z, = 2 + i , z2 = 1 + 3i, z3 = -4i and z, = 2 – 3i.Evaluate (i) z,² – z3 + 6i 1)…

A:

Q: Problem 9. Determine whether cach of the following two statements is true or false. If a statement…

A:

Q: Question 2. Suppose that r + y3 and x, y, z are positive integers. Show that one of the three must…

A: We use elementary number theory, in particular Legendre's symbol and congruence to solve this…

Q: Problem 4. Does there exists a solution xE Z to the equation 3x2 + 11x = -23 mod 61?

A:

Q: 1. In(4 + 7i)4i

A: Question (1) - Let the given value be y - y = ln4+7i4iy = 4iln4+7i          ........(1)…

Q: Question 37 VE245 and What is the product of v 22- and (2+6i) 1+2i -4+8i C) -2+8i (D) 1-21

A: Product of complex numbers

Q: Perform the computations in the given question and express the results in standard form a+ bi. (5 -…

A: The standard form is  a+biSo,(5−3i)(2−4i)=10−8i-6i+12i2

Q: The product (6+2i)(4–3i) can be written as (1) 24– 6i (3) 2+5i (2) 18+10i (4) 30-10i

A: Given equation (6+2i)(4-3i)=6(4-3i)+2i(4-3i)  = 24-18i+8i-6i2  = 24-10i +6         [∴ i2= (-1)]  =…

Q: The result of the operation (3–2i)(2+3i) 3-4i is: Select one: ; 63 25 16 25 16 63 25 25 63 + i 25 16…

A:

Q: Perform the computations in the given question and express the results in standard form a+ bi.…

A: The given complex expression is, 5+2i5-2i The objective is to write the expression in standard form…

Q: Show ther' 3 2

A:

Q: Regarding Equations 11-20, 11-21 and 11-23, we could alternatively reject Ho if the resulting…

A: Since we know that When p-value < α Then we reject the null hypothesis And, when When p-value…

Q: Perform the computations in the given question and express the results in standard form a+ bi.…

A: 13+i=13+i×3-i3-i=3-i32-i2