If z isa complex number satisfying|z-1=1. Then prove that z-2 = i tan {arg (z)} -itar

Q: Determine the fifth roots of z = (4-j5)cos(1+j3). Express your answer in rectangular form

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Q: 2. If z = cos 0 + i sin 0 where 0 is real, show that 1 1 - i tan- = - 1+z 2z 1-z2 Express: а) 1+z2…

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Q: If zisa complex number satisfying |z-1=1. z-2 Then provethat-i tan{arg (z)}

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Q: If z1,72,., are complex numbers such that = =.==,| =1,Prove that 1. 1 1

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Q: B- If x+= = 2 cos Ø prove that x"+ 2 cos rø by used complex number.

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Q: Prove that (1+i)" +1(1-i)" = 2 cos %3D

A: We will solve the following

Q: using De-Moivre's theorem prove that cos π/7, cos 3π/7 and cos 5π/7 are the roots of 8x3-4x2-4x+1=0.…

A: The given equation 8x3-4x2-4x+1=0 Roots of the equation are cosπ7, cos3π7, cos5π7 use trigonometric…

Q: express  in the form z = x +yi the complex number z whose modulus and argument are given.  |z| =…

A: z= x+iyz=12,    arg(2) =-π3modulus of z =z = x2+y2 =12⇒x2+y2 =12     -(i)

Q: Let z be a complex number. Then the solution(s) of sinhz+coshz=1/e is (are) O z=2nti-1 where n is an…

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Q: Find the indicated power using De Moivre's Theorem. (Express your fully simplified answer in the…

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Q: We consider the Complex numbers x,y, z with modulus 1 with the property that: x + y + z = 0 and the…

A: Trigonometry is a branch of mathematics that studies relationships between side lengths and angles…

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: The set of all complex numbers is denoted by C={x+iy:x,yER} ylgn O ihi O السؤال 2 lim does not exist…

A: Every complex number is x + y i , where x and y are real number So statement is True.

Q: 4. If the two complex numbers z1=ri(cos01+ i sin 01) and z2= r2(cos 02+ i sin 02) then the numbers…

A: The given complex numbers,z1=r1cosθ1+i sinθ1 and z2=r2cosθ2+i sinθ2

Q: B- If x+ 2 cos0 prove that x" +2 cosro by used complex number.

A: we have to show that the following

Q: Let z be a complex number. Then the solution(s) of sinhz+coshz=1/e is (are) z=2nti-1 where n is an…

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Q: 67 V3 1 Use De Moivre's Theorem to express the complex number on the form a+ bi. ---1

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Q: a) Show that the modulus of sum or difference of two complex numbers is always less than or equal to…

A: Use the properties of complex numbers to solve this problem as in next.

Q: Let A be a fixed constant positive number and f be an entire function with the property that |f (z)|…

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Q: Let z1 = r1(cos θ1 + i sin θ1) and z2 = r2(cos θ2 + i sin θ2) be complex numbers, then the…

A: Given that, z1=r1cosθ1+isinθ1z2=r2cosθ2+isinθ2

Q: i) Find an upper bound for the modulus 3z³ + 5z + 1, if |z|<1 where z is the complex number.

A: Now for the mod function: : a+b≤a+b. SO using the same method in the given complex function:…

Q: Find the modulus and argument of the following complex number. z=(3-2j) (1+2j), giving the principal…

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Q: The th roots ofz=a+ bi whenk=0, 1, ..., n-1. take the form: 0+2n COS 0+2n +i sin O [cos(0+ 2kx) +i…

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Q: Let z be a complex number .then cos (3z)-I bounded or not

A: Substitute z=x+iy, then convert into real and get known real valued function which is unbounded.

Q: p and q are complex numbers such that pl = 7√3 and lp + ql = 12√2. - On what interval must q fall…

A: Use  Cauchy inequalities and solve the question.

Q: Find the indicated power using De Moivre's Theorem. (Express your fully simplified answer in the…

A: The given expression is 22+22i20.

Q: For complex number z and w, prove that zw-wz=z - w if and only if z =w or, zw = 1.

A: We know that , for a complex number|z|2=zz¯and when z is a real numberz=z¯

Q: Given that z = cos + isin and u-iv-(1+z)(1-22). Show that 30 v = utan 2 r = 4² cos² (2). where r is…

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

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Q: Let z be a complex number. Then the solution(s) of sinhz+coshz=1/e is (are) * z=nti-1 where n is an…

A: This is a problem of complex analysis.

Q: Exercise 5. Let z=x+iy be a complex number such that cos (3z) # 0. Then Re(tan(3z)) is equal to…

A: No matching answer found

Q: cos z = cos x cosh y– jsin x sinh y

A: Complex numbers

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

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Q: Let z=x+iy be a complex number such that coshz #0. Then Re(tanhz) is equal to

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Q: B- If x+! += 2 cos prove that x"+= 2 cos rø by used complex number.

A: we have to show that the following

Q: Express in exponential form: –8 + 8i/3. 31 Represent graphically the set of values of z for which <…

A: -8+8i3

Q: Let z be a complex number. Then tanh(2+JTi) is equal to cothz -cothz None of these -tanhz O tanhz O…

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Q: Let z=x+iy be a complex number such that coshz#0. Then Im(tanhz) is equal to

A: None of these is correct.

Q: tane – cot0 a. Prove 1- 2cos?0 6. Show 1 – 8sin20 · cos²0 = cos(40) %3D 5. tane + cot0

A: To prove the given identities.

Q: 22. Given that Z= 2-3i, express Z/Z* and Z(cos-- isin -) in the form a + bi, where a and b are real…

A: Note: "Since you have asked two questions, we will solve the first question for you. If you want any…

Q: Prove that (1+i)" + 1(1- i)" = 2m/2*1 nt cos 4

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Q: Find the indicated power using De Moivre's Theorem. (Express your fully simplified answer in the…

A: Given expression is (23+2i)-5 We have to use De Moiver's theorem to simplified the answer in the…

Q: Find all complex numbers z satisfying = -i

A: i = -1(i)2 = -1

Q: Prove that (a) Pn (cos 0) = 2F1(-n,n+ 1; 1; sin²0/2).

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Q: Let z be a non-zero complex number. D if OsArg(z)sTt/2 D for all complex numbers D if OsArg(z)sn…

A: we know that logzn≠nlogz for all complex numbers. Since ew=z and -π&lt;Imw≤π If w=logz, nw is a…

Q: Let z be a complex number. Then the solution(s) of sinhz+coshz=e is (are) * does not exist z=nti+1…

A: Given that z is a complex number. we have to find such z so that                              sinh…

Q: or complex number z and w, prove that zf w-|wfz=z-wif and onlyif z = w or, zw = 1. W

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Q: Let z be a complex number. Then cos(72)+3i is unbounded in C.

A: A complex no. in the form of a+ ib

Q: p and q are complex numbers such that |a| = 4√5 and lp + ql = 9√/2. - On what interval must lp fall…

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