7. Find the modulus and argument of -7 + 8i. Hence, express (-7+ 8i)8 in the form x + yi.

Q: (1) (1 + v3i)} Place all answers in the following blank, separated by commas: (2) (1 + i)} Place all…

A: 1. (1+3i)13 2. 1+i123. 5i1+i16

Q: Find the solution to 34x = 77(mod 89) that is positive and less than 89.

A: given that                                          34x≡77 (mod 89) we have to find positive…

Q: 2n-1 b) Prove that if , r #1 (mod 2"), then n is even.

A: Given that x2n-1≢1mod2n . The objective is to show that n is even. The x2n-1≢1mod2n can be written…

Q: (3). (a). Find all solutions to the congruence 6x = 9 (mod 45)

A: To Determine :-  All solutions to the congruence : 6x ≡ 9   mod 45 .

Q: How many square roots of 3 (mod 1001) are there? (Hint: 1001 = 7 * 11 * 13)

A:

Q: Find all integer solutions satisfying all the equations given. 5x =1 mod 39 3x =1 mod 25 4x =1 mod…

A: Concept :.   *   ax =6 mod n                           g (d (a,n) = d (let)…

Q: Find all values of x (using congruent notation) for 35x ≅ 3 (mod 89)

A:

Q: Find all solutions in {0, 1,2, ..., 12} to x26 + 15x13 = 12 mod 13.

A:

Q: (1) Consider the equation 2.x +1 = 0 mod n. For which n are there no solutions? one solution?…

A: Congruence

Q: Find in modulus-argument form [(1+iv3)³/ E-1+i)²]°.

A:

Q: (b) Show that įn is real, even though i or 9i is not.

A:

Q: a + bi form modulus argument 7 210° 5 135°

A:

Q: Find the modulus and argument of the com

A: Given,          7-xi5+3i2 and  x = 2.

Q: 5. Use the method of successive squaring to compute 3875 (mod 103) 1

A:

Q: and 10 9. Use Euler's theorem to evaluate 2100000 (mod 77). An11

A:

Q: 1. Give the ten 10th roots of unity. Write them in the form e. Among these 1Oth roots, which are the…

A: According to Bartleby's guidelines, we are allowed to answer only one question at a time. So here is…

Q: (a) Find two integers satisfying the equation r³ + 24x² – 2 = 0 mod 23.

A:

Q: QUESTION 4 Find two integers, x, where -3 < x < 12 such that x =4 mod 6 X = and x = YOU MUST SHOW…

A:

Q: Determine if the statement sin z = 6 is possible for some real number z.

A: The detailed explained answer is given below-

Q: 4. Find the modulus and argument of z = -2-2i"

A: Modulus of a Complex Number: Let z = x + iy is a complex number. A complex number represents a point…

Q: (2) (a) Find all of the solutions modulo 15 to 6x = 15 mod 18. Express your answer in terms of the…

A: Given, 6x≡15 mod 18. As it is known that, an≡bn mod cn ⇔ a≡b mod c. Therefore, we have 6x≡15 mod 18…

Q: Only one prime of the form1+4n exists. Determine this prime number and prove it's the only one of…

A: A number that is greater than 1 is said to be prime if it has only two factors 1 and the number…

Q: Find an integer A so that: A79 = 7 (mod 277) Please solve step by step thanks!

A: Given an equation. Let's solve for A.

Q: Find a number a such that 70a = 1 mod 17.

A:

Q: 24. What are the modulus and the principal argument of the -4 + 4i? *

A: Here given complex number as z = -4+4 iThus modules of this complex number is z = (-4)2+42…

Q: Find the modulus and argument of 2V3+i 1-23i 1+2i (ii) 1-3i

A:

Q: Find the modulus and argument of 5 - 7i.

A: Since the modulus of a complex number a+ib is |a+ib|=a2+b2. So, the modulus of 5-7i is…

Q: Solve the congruence x² = 9 (mod 600).

A: Given congruence is x2≡9 mod 600

Q: 3. Find the residue of 20211202 mod2022 using Euler's Theorem.

A:

Q: The equation 82x = 12 (mod 13) has O 1 incongruent solution modulo 12 O 4 incongruent solutions…

A: First Option Is Correct Answer.

Q: Find an integer x that satisfies the equation. 5* = 4(mod 11) 17x?=10(mod 29) i. %3D ii.

A:

Q: B. Using Fermat's Theorem •Determine all solutions of the equation 6x = 18 in Z24. •Describe all…

A:

Q: Find the mod of (2-4i)^1/2

A:

Q: 3. Let AC BCR. Prove ACB.

A:

Q: What is the modulus and argument of -3. Select all that apply

A:

Q: 3.2.6 Find all solutions x to the congruence equation 12x = 1 (mod 17)

A: Given, 12x = 1 (mod 17) So, 7•12x = 7•1 (mod 17) So, 84x = 7 (mod 17)

Q: solve by means of a derivation, the congrucnce equation; 10x= 4 (mod 2a) Express ansurer in form X=…

A:

Q: What set of numbers does 10i belong to?

A: given,         What set of numbers does 10i belong to?

Q: Express each of the following in the form a + bi. 4. cosh(1-12)

A:

Q: #1. Find all five 5" root of Z = 32cis40° 5th

A: Given z= 32 cis 40° rewrite it as z= 32cos 40+isin 40 if z= rcos θ+isin θ then n distinct complex…

Q: 1) Write all the following as expansi > 0-2 > V26 V35

A: In this question we have to do expansion.

Q: How many multiplicity of - 1 are there in the roots of x +3x2 + 3x+1 0? O 1 O 2 3 O 4

A: Given equation  x3+3x2+3x+1=0

Q: Does

A:

Q: Does ?2 ≡ 23 (mod 79) have any solutions. Justify your answer using the Legendre symbol.

A: Note that the congruence X^2= 23 (mod 79) will have solution if and only if 23 is a quadratic…

Q: (a) Find an integer r E {0,..., 196} which solves the equation 167 = 7 (mod 197).

A: Given equation is x157≡7mod197. We have to find that an integer x∈0,....,196 which solves the…

Q: 6. Find a prime number p for which the equation x² = -1 mod p has no solution.

A: Given is a  modular equation.   To Find: A prime number p such that the given equation has no…

Q: 2. Find the exact value of: of:[2cis ] [3cis 5]

A:

Q: What is the modulus and argument of 3i.

A: Let z be a complex number then, z is written as z=x+ιywhere x and y are real numbers.We have to find…