Exercise 1. Let z be a complex number. Then e3z+i is bounded over the set of complex numbers. a. True b. False Exercise 2. Let z be a complex number. Then cot(5z – 1) is equal to a. cot(5z) b. coth(5z) c. -tanh(5z) d. -tan(5z) e. None of these Exercise 3. Let z be a complex number. Then i(cosh(3z) + sinh(3z)) a. ie3z b. ie-32 c. e3z d. None of these Exercise 4. Log(1 - iy3)? =

Q: Q: For any two complex numbers z, and zz, prove that z-z|+|z+!z|=z-z-2+z-z+

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Q: Let z is a complex number and Z is the conjugate number of z then () equals O a. z1 Z2 b. 21 Z2 C. O…

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Q: - Let a1, a2,..., an be nonzero complex numbers. Find 0 0 0 0 : 0 an a1 0 0 a2 : 00 : 0 0 : ... ...…

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Q: Let z be a complex number, and w be its additive inverse. Let c be another complex number. If |zc| =…

A: Given z be a complex number and let w be its additive inverse. ⇒z+w=0 and z=w, argz=argw+π Given…

Q: Consider the Ealleming eqration - Waez Comples nasm ber if yex js a Line on Paye z What is written…

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Q: A. Write T if the statement is TRUE and F if the statement is FALSE, then justify your answer in…

A: Polar form of a complex number: In polar form, complex numbers are represented as the combination of…

Q: How may the following complex numbers be obtained fromz = x + iy geometrically? Sketch. 1 / z

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Q: 2) Consider complex numbers z₁ = 4-3i and z₂ = −6+4i and compute a. Z₁ Z₂ b. 21 Zz C. Z1

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Q: 3.21. A quarternion is an ordered pair of complex numbers; e.g., ((1,2), (3, 4)) and (2+i, 1-i). The…

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Q: Let z be a complex number with |z = 11 and let z0 = 17 – 20i. What is |z – z0| + |z+ zo|??

A: Given:- Let z be complex number with |z| =11 and z0 =17 -20i  To find:- value of |z - z0 |2 +  |z…

Q: Find the cubic roots of the Complex number Z=-j and graph these roots in the complex Plane? Ans. Wo…

A: To find cube root of given complex number first convert into euler form then take cube root. Then…

Q: IN! Write each complex number in standard form. 4 10. 25 Choices for 10-16: 1 A) 11. B) C) -- 49 D)…

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Q: Let z be a complex number. Then cos(32)-i is unbounded in C. * False True

A: use:- cos(x+iy)=cosxcoshy−isinxsinhy

Q: Justify your answer. Say if its true or false 1.- If z1, z2 and z3 are complex numbers such that…

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Q: 6. Find the following complex numbers in the form r+ iy, whe and y are real. (i) (3+7i) + (6 – 10i)…

A: we have to find complex numbers in the form of x + i y  Adding real part with real part and…

Q: Let z be a complex number. Then coth(2+7ti) is equal to cothz -cothz tanhz None of these -tanhz

A: Solution

Q: Let A, B, C be the set of complex numbers defined as: A = {z: | z+2|-|z- 2 || = 2} 6. %3D z-1 TC B =…

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Q: 8. Consider the complex number z = 2 + i and w = 7 – 2i. Write down the real and imaginary parts of…

A: Given : The complex numbers z = 2 + i  and w  = 7 - 2i.   To write the real and imaginary parts of…

Q: Let 21, 22,..., 21011 be complex numbers such that 2₁ +22+...+ 21011 = 0 and |21| = |22| = = |21011|…

A: Aim:  To prove, 1+z12 + 1+z22 + ...+ 1+z10112 = 2022Given: 1. z1 + z2 + ...+ z1011 = 02. z1 =  z2=…

Q: Prove: Ifz₁, Z₂,..., Zn are complex numbers, then Z₁ + Z₂ + +Z₁₁ = Z₁ + Z₂ + ... + Z₁₂ A

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Q: If Zo is any complex number interior to any simple closed contour C prove that dz 2πί, η -1 c…

A: Let C be a simple closed contour and let z0 be a complex number inside C. Prove that:…

Q: Show this sets in the complex plane. 6 = {z: - sag (2+1-1) 632/2/ H>{*: 1418142, A Lorgt < 32 )

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