For Exercises 9–14, find the modulus of each complex number. (See Example 2) 9. а. 20 - 21i b. -11 + 60i 10. a. 5 + 12i b. 7 - 24i 11. а. 4 6i b. -5 + 5i 12. a. -14 + 6i b. 3 + 9i 1 13. a. 3 2 3 b. - + -i 3 8 V3. b. -1 + 14. a. 2i 3 Too 2.

Q: Assume that u - v = 2, ||u|| = 8, and ||v|| = 3. Calculate the value of (9u + v) · (u – 8v). %3D…

A: we multiply the given equation and then put the value of given data. u=8 v=3 u.v =2 note- According…

Q: Prove that Eo 2i = 2n+1 – 1 - i3D0

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Q: 17. Given a = 4 – 4i and az = 4 + 3i, express %3D :11 in the form a + bi. a, az CLONE Dec 19

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Q: Show that 1 Σ (z – n)2 cosec² (z) 8.

A: As we all know the theorem which states that, For z∈ℂ\ πℤ 1sinz=∑n=-∞∞-1nz-nπ=1z+2z∑n=1∞-1nz2-n2π2…

Q: Q1. Prove that for any natural number n, E, 2i = 2n+1 – 1. i%3D0

A: I have used mathematical induction to prove the result

Q: What is the modulus of: 1. (i + 1) (2 - i) 2. 4 + √5i 3. 2 - 3i

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Q: 5. If Z1 = V3 - 2i, Z2 = -i+1 and Z - 3= 4i – 2. Evaluate (i) Re{3Z -5Z +2Z}} (ii) |(1+ Z, + Z3)(i –…

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

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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 elements are in Z5[i]/<1 + i>?

A: Given Data The expression is Z5[i]/<1+i>.   Consider the Z5[i]/<1+i> in the form of…

Q: Show that 1/2 1+ 72 2 1. i%3D1 Xi n-1

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Q: 11. What theorem is used to prove that BD 1 AC? C В. D A

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Q: Show that the sun of the odd numbers 1+3+5+7+9(2n+1)=n^2

A: We have to prove this using arithmetic mean  In this a = 1 which is first term  And common…

Q: 61. Prove Theorem 4.13(c): For any real numbers a and b, Si x² dx = (b³ – a³). Use the proof of…

A: To prove : for any real numbers a and b,∫abx2dx=13(b3-a3). Solution: We know, ∫xndx=xn+1n+1+C…

Q: Prove that Ek=0 C) 7n-k . 2k = 32n %3D

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Q: 3. Show that (1+i) = 2i

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Q: 5. If Z1 = V3 – 2i, Z2 = -i+1 and Z3 = 4i – 2. Evaluate (i) Re{3Z} – 5Z7 + 2Z}} (ii) |(1+ Z2+ Z3)(i…

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Q: Let 2 3 0 1 1 1 1 3 A = 1 -2 1 -3 1 В 1 and C = |0 -2 -2 -1 1 1 1 -3 1 | Find an elementary…

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

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Q: CALCULATE THE FOLLOWING USING MINOR COFACTOR AND COFACTOR EXPANSION 3 -8 2 A= 2 -6 3 4 4 2

A: A system of m×n numbers arranged in the form of a rectangular array having m rows and n columns is…

Q: Find the conjugate and modulus of the following: (i) (1 + i³) – (4 + 3i) + (7 – 9i*) (ii) 7 +i° + (6…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: 13. Find another representation 2, in which 3 a. ris negative and 0 < 0 < 2T; b. ris positive and…

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Q: If A= B = verify that A(B + C) = AB+ AC. :) 1 If A = 2 and B show that (AB)" =B'AT 4 -1

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Q: 6a. Prove by mathematical induction: n Vn E N, > i! - (1? + 1) = (n + 1)! - n i=1

A: To prove that given statmenent by mathematical induction

Q: 2. If A = 2i + 2j-k and B 3i-6j + 2k, find (i) AB and (ii) AX B.

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Q: 38) - con A) 0 sec B) 5π T, 13л 5т D) 0 3 12 12

A: Find the value of x which satisfy sec(x/2)=cos(x/2)

Q: a) If Z1 = -3 + 3i and Z2 = 4i. Show that: i) Arg(Z,Z2) + Arg(Z,) + Arg(Z2) ii) Arg (2) = Arg(Z,) –…

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Q: The formula in cell C2 is = A$2. Auto fill is used by dragging C2's auto fill box across to D2, E2,…

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Q: In(z,) + In(-v3 – 1) = In(2) +i %3D

A: Answer

Q: 4i then what is Re(

A: Given: z=3+4i. To find: Rezz¯.

Q: 2. Show that coo(N) co(N) § c(N) Ę e^(N).

A: To prove that c00N⊂c0N⊂cN⊂l∞N. By definition, c00=x∈lp|all but finitely many xj's are zeroc=x∈l∞|xj…

Q: The modulus of 5 + 4i is * O-41 O-√41 O√41 041 The conjugate of (i-i²)³ is O-2-21 2+2i -2+2i Oi-1

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

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Q: (Chapter 3.2. Ex.# 49) Show that if fi(x) is O(g1 (x)), f2(x) is O(92(r)), and f2(r) # 0 and g2(r) #…

A: Given: If f1x is ⊝g1x, f2x is ⊝g2x, and f2x≠0 and g2x≠0 for all real numbers x&gt;0.

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

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Q: Use Gauss's trick to determine H(n)=1+5+9+13+...(4n-7)+(4n-3)+(4n+1) I got n(4n+2)/2 is this…

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Q: 3. Show that a2 + b2 + c2 > ab + bc + ca and using this result show that (a) (a + b + c)2 > 3(ab +…

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Q: Examplen' find the pvoduct of the follow ing (wo natricesi 2. 2. ら 1. 又3 3.

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Q: What is the midpoint between z1 = 3 + 9i and z2 = 4 - 12i? (0.5,-10.5) (3.5,-1.5) (-2,-2.5) (6,-1.5)

A: Explanation of the answer is as follows

Q: A (0, 8) В (4, -12) С (9, -1) D (-8, -8) Е (1,-3) F (3, 5) ULLV 1. Identify the component form of…

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

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Q: (2.5) Find another representation in which a. r is negative and °<0 < 2n. b. ris positive and -2n <0…

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Q: Show that, for any complex number z, zz = |2|², z+z = 2Re(z) and Re(z) < |z|. Henc show that i. [21…

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Q: 5. Compute for the product of the complex coardinates :(3, 1)(3, - 1) a. (2,1) b. (1,1) c. (3,1) d.…

A: The given problem is to find the product of the given complex coordinates, We have to use product of…

Q: Suppose z = -18 + 14i and w 16 + -13i. Then Re (z + w) =? %3D

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Q: (2.) Find another representation in which a. r is negative and 0 <0 < 2n. b. ris positive and -2n <0…

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Q: re + e Show that 1. 2

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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…

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Q: 2. In figure, ZDBA = 132° and ZEAC = 120°. Show that AB>AC. E 132 D B 120* C

A: Given m∠DBA=132°,m∠EAC=120°