Let z be a complex number. Then the solution(s) of sinhz+coshz-e is (are)* None of these z=nti+1 where n is an integer. O z=1 O z=2nti+1 where n is an integer. O does not exist

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

A:

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

A:

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

A:

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: 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: 1. Consider the nonzero complex numbers 21 5i z2 = 4i and z3 (z1 + z2 + 23) (a) Evaluate (z1 22 Z3)…

A:

Q: Let z be a complex number. Then the solution(s) of sinhz+coshz=D1/e is (are) * O z=2nni-1 where n is…

A:

Q: 1. Consider the nonzero complex numbers z1 = 3i, z2 = 6i and z3 = 4i. (a) Evaluate (z,z,z3) (1 + z2…

A:

Q: Let , ² be the complex cube roots of unity. Let z₁, Z₂, Z3 be complex numbers such that Z₁ + Z₂ +Z₁…

A: Given that, Let ω,ω2 be the complex cube roots of unity. Let z1,z2,z3 be complex numbers such that…

Q: A if z, and z, are complex numbers Z2 Show that ()= Z 22

A:

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: Let z be a complex number. Then the solution(s) of sinhz+coshz=1/e is (are) * O None of these O does…

A:

Q: Let z be a complex number. Then the solution(s) of sinhz+coshz=e is (are) * O None of these O…

A:

Q: 1. Determine all the complex numbers for which f(z) = Log(z – 1+ 2i) is differentiable. |

A: Since you have posted multiple questions. I am answering the first one. Please post the question…

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

A:

Q: 4. Let a be a complex number. Show that equation |z – al + |z +a| = 2 %3D admits a complex solution…

A: Given equation is |z-a|+|z+a|=2    (1) since a is complex number. let  z=x+iya=c+id

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…

A:

Q: 3) The complex conjugate of z is denoted as z. Solve for z in the equation: 27(1 – j2), j 2- j3 1 +…

A:

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 C be a fixed nonzero complex number and note that i is a multiple valued, what restriction must…

A:

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…

A: The standard  from of a complex number is given by z=a+ib, where a,b are two real numbers and i=-1.…

Q: 11a Express the complex number z 10 cis in 6. rectangular form a + bi.

A: Given problem is :

Q: 1. Consider the nonzero complex numbers z, = 2i, zz = 8i and z; = 7i. (a) Evaluate (z,z,z,) (2) +2,…

A: Introduction: In most cases, the primary value Arg(z) of a complex number z=x+iy is equal…

Q: 1. If z = 1+ iy is a complex number. Use the exponential form to compute (1+ /3 i)201

A: Definition used -            DeMoivre's theorem -             For a complex number z=r(cosθ+isinθ)…

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: If z1, Z2, Z3 are complex numbers such that |z| = |z2| = |Z3| = %3D 1 1 = 1, then |z, +z, + z,| iS

A: Introduction :

Q: If zi and z2 are two distinct non-zero complex numbers such. that |z|| = |z2), then 2 +Z, is always…

A:

Q: 3) The complex conjugate of z is denoted as z. Solve for z in the equation: 27(1- j2) j 2-j3 1+ j2…

A:

Q: 3. Having two complex numbers z1 & z2, with product z,z2 being real and non-zero, verify if there…

A: Answer is following .

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: Use Bombelli’s approach to find a complex number c = a + bi such that c3= 18 + 26i where a and b are…

A:

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

A:

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: Use formula of hyperbolic function.

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: 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: 3) The complex conjugate of z is denoted as z. Solve for z in the equation: 27(1- j2) j 2- j3 5z 1+…

A:

Q: 1. Consider the nonzero complex numbers ž1 = 7i, 22 = 8i and z3 = 8i. (21 + z2 + z3) (a) Evaluate…

A:

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

A:

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

A:

Q: [1E q22] Question is attached, Thanks ?

A: To prove the equality of the two angles , under the given conditions

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

A: Given, z be a complex number. we need to find the solution of sinhz+coshz=1e

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 the solution(s) of sinhz+coshz=e is (are) * O z=1 None of these does…

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)

Q: 4 9) Use Euler's formula to compute (--i. Express as a 2 2 complex number of the form a + bi.

A: