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

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 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 z be a complex number Then the solution(s) of sinhzicoshz31/e is (are) None of these. does not…

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Q: 4.Find all complex numbers of the form z=a+bi, where a and b are real numbers such that zz = 25 and…

A: To find out all the complex numbers for the given condition.

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 a complex number z satisfies z = z-1, what can be said about the number? Are con Nay/ Say that…

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Q: The set of all complex numbers is denoted by C={x+iy:x,yER} ylgn O ihi O

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

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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: Prove that there is no complex number z such that 1 |z|«anda,z' = 1, where|a,| < 2. 3 r=1

A: In this question we have to prove that there is no complex number z such that z&lt;13 and ∑r=1n…

Q: if (1+i)(x+iy) = 2+4i then 5x is: * O 15 O 10 05 O 3 Let z be a complex number such that |z| = 4 and…

A: Given (1+i)(x+iy)=2+4i. We find 5x.

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 z be a complex number such that |z|=1, that is z∙z ̅=1. Compute 〖|1+z|〗^2+〖|1-z|〗^2.

A: Given that -  |z| = 1 we have to compute the following -  1+z2 + 1-z2

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

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Q: 10. Find a complex number z such that (a) z – z+7 – 6i = 0 - | (b) = 3 + 4i %3D 1+ z

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Q: if (1+i)(x+iy) = 2+4i then 5x is : * O 15 O 10 O 5 O 3 Let z be a complex number such that |z| = 4…

A: To find the value of 5x:

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 cos(3z)-i is unbounded in C. * False O True

A: From Liovilles thm we can say Every non constant entire function is unbounded.

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

A: The last option is correct.

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: Let z be a non-zero complex number. Then Log(z²) = 2Logz for all complex numbers O if OSArg(z)ST/2 O…

A: We know that  log(z1.z2) =logz1 +logz2 iff -pi&lt;arg(z1) +arg(z2) &lt;pi

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: Let z be a complex number. Then sinh(2z)-i is bounded in C.* False True

A: Given a statement

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: For every real number a > 0, Find all complex numbers z, sati sfying the equati on z|-|+ a +i= 0.

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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…

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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 satisfying 12|z|² = 2|z + 2|² + |z² + 1|² + 31. What is the value of z +-?…

A: Given that Let z be a complex number satisfying  12z2=2z+22+z2+12+31 To find the value of z+6z

Q: A. Express the following complex numbers in standard form. 1. z = 0 + 2.1=-2+4 2

A: Introduction: There are many different representations of a complex number. But, the standard…

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: 5. Find all complex numbers of the form z = a + bi , where a and b are real numbers such that zz' =…

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

A: Assume sin3z is bounded. We know that sin3z is analytic on C, that is sin3z is an entire function.…

Q: Find a complex number z=a+bi such that z*z_1=1. Also, convert z into its three (3) other forms.…

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

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Q: Let z be a non-zero complex number. Then Log(z²) = 2Logz O if OsArg(z)sn O if -T/2<Arg(z)s0 for all…

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Q: 3.5. If |2| = 1, then show that az + b 1 bz +a for all complex numbers a and b. ||

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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: The set of all complex numbers z such that |z – 1| 2 is

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

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Q: Let z be a complex number. Then sinh(2z)-i is bounded in C. * False True

A: