Let z be a complex number. Then Im(-iz+1)= * O =liz-1| O None of these Ozliz-1| Sliz-1|

Q: If z₁ and z₂ are arbitrary complex numbers, prove that (22₂)=(3)(2)

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Q: Find all complex numbers z satisfying 4 = -81

A: Find all the complex numbers z satisfying z4= -81

Q: Let z be a complex number. Then sin(3z)-i is bounded in C. * True False

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Q: Let z be a complex number. Then sin(3z)-i is bounded in C. * False True

A: See solution below

Q: Let z be a non-zero complex number. Then Log(z²) = 2Logz O if -n/2<Arg(z)<0 O if -TSArg(z)<0 for all…

A: For Real number we have Log(x2)=2Log (x) but for complex number z the equality is not true . For…

Q: Let z be a non-zero complex number. Then Log(z²) = 2Logz O None of these O if OSArg(z)<T/2 O if…

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Q: Show that there exists a complex number z such that z" +cos(| z |):(1+31z*)=0

A: The complete solutions are given below

Q: If z1 and z2 are complex numbers such that |21| = |2|, prove that arg(2122) = arg ((21 + z2)²) .

A: This  problem is related with complex analysis. Given that z1 and z2 are two complex numbers such…

Q: Let z be a complex number. Then cos(5z)+i is bounded in C.* O False True

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Q: If z,,z, are two complex numbers then: ||z.|-|z2||>|z,-z z. +z_ s z +z]. z +z_ = z +/z

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Q: Let z be a complex number. Then cos(3z)-i is unbounded in C. O True O False

A: Use z=x+iy, then show it is bounded.

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…

A:

Q: The set of all complex numbers is denoted by C={x+iy:x,y ER} 0 صواب İhi O السؤال 2 lim does not…

A: Complex numbers: A complex number is represented in the form a+ιb, where a and b are real numbers,…

Q: Let z1, z2 be two complex nu numbers. Prove that z, and z

A: Complex numbers: The sum of a real and an imaginary number is a complex number. A complex number is…

Q: 2. Find the general value of z in the complex number : - jl O A. J[(2/3)nk+ Tt/6] O B. J[(2/3)nk -…

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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: Let a and z be complex numbers with |a| # 1 and |2| = 1. %3D z - a āz – 1 Show that w= satisfies |w|…

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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: Let z be a non-zero complex number. Then Log(z²) = 2Logz O if -T/2<Arg(z)<0 O if OsArg(z)sTI None of…

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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: 3. Determine all complex numbers z for which |2z – 1| < 2|2 – i|.

A: The given problem is to find all the complex numbers that satisfies the given complex inequality.

Q: If z is a complex number, show that the product of z and its conjugate is a realnumber.

A: Let z=a+ib be any complex number where a and b are real number. Then conjugate of z is z¯=a-ib

Q: a) Let a complex number z =-5i+3. Find in the standard form x+ yi . IN

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Q: Let z be a complex number. Then Im(-iz+1) = * O =liz-1| None of these O zliz-1| O sliz-1| OOO

A: Let z be complex number then

Q: Let z be a non-zero complex number. Then Log(z²) 2Logz if -TsArg(z)<0 for all complex numbers if…

A: The general logarithms theorems hold for argument is within 1st and 2nd quadrant s

Q: Write down the definition of the complex conjugate, z, of z = a + ib where a, b are real numbers.…

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Q: bers are conjugate. If z, and z2 are two non-zero complex numbers st jal arg (2) ) - arg (z2 ).

A: Since we know that, | Z1 + Z2 | = |Z1| + |Z2| only when the the point Z1 , Z2 and origin are…

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 be a complex number. Then coth(2+ Ti) is equal to O None of these O -cothz O cothz O tanhz O…

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Q: 13 Jlgull If z,,z, are two complex numbers then:

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Q: The polar form of the complex number –3/3 + 3i is 6(cos(150°) + isen(150°)) 6(cos(300°) +…

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Q: Let z be a complex number. Then Im(-iz+1)= O None of these O sliz-1| O =liz-1| O 2liz-1|

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Let z be a non-zero complex number. Then Log(z²) = 2Logz O None of these O if -T/2<Arg(z)<0 for all…

A: z&gt;0 &amp; z^2&gt;0 are must to define the given logarithmic equation.

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

A: I have solved bothe examples for first question first option is correct And for second question last…

Q: Let z and w be complex numbers such that |z|= 1 and |w| # 1. Prove that = 1. - zw

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Q: Let z be a complex number. Then the solution(s) of sinhz2+coshz=1/e is (are) * O z=2nni-1 where n is…

A: Solution:

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…

A:

Q: Let z be a non-zero complex number. Then Log(z²) = 2Logz O if OSArg(z)STM O if -nSArg(z)0 O None of…

A:

Q: Let z be a complex number. Then Im(-iz+1)= * O =liz-1| None of these O 2liz-1| <liz-1|

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Q: Let z be a complex number. Then sin(3z)-i is bounded in C. False True

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

A: this is true , because

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

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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: 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: Let z be a complex number. Then Im(-iz+1)= O None of these O sliz-1| =liz-1| O zliz-1| O O O

A: Given problem is :

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

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Q: Let z be a complex number such that Iz| = 4 and arg(z) = 5Tt/6, %3D * = then z

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Q: Let z be a non-zero complex number. Then Log(z²) = 2Logz O if -TSArg(z)<0 O None of these O for all…

A:

Q: Let z be a non-zero complex number. Then Log(z²) = 2Logz for all complex numbers None of these if…

A: Given log(z2)=2log(z)