Let z be a non-zero complex number. D if OsArg(z)sTt/2 D for all complex numbers D if OsArg(z)sn DNone of these if -nsArg(z)<0

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

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

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

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Q: Let a, b, and c be any three nonzero complex numbers. If |z| = 1 and 'z' satisfies the equation az +…

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Q: We assign a complex number Am to each n-tuple of non-negative integers m = (m₁, ..., mn)…

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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 non-zero complex number. Then Log(z²) = 2Logz %3D O if -nsArg(z)s0 O None of these O if…

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

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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…

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

A: We can come out with an answer by Liouville's Theorem, It states that a bounded holomorphic function…

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

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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: For any complex numbers z1 and z2 prove that |z1z2| = |z1||z2|.

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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: 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: For all complex numbers Zq,Z2 prove that |z, +z2| <]z|+]z2l

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Q: Let z be a non-zero complex number. Then Log(z) = 2Logz %3! for all complex numbers if OsArg(z)sT/2…

A: By arguments written in step 2

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

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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 3 be a complex number algebraic Q. Prove that 3i is algebraic Q. over over

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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…

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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 z₁,z, and z, be complex numbers such that |z₁|=|z₂|=|z₁|=|z₁+z₂+z₁|= 2. If and z₂ #z,. Then find…

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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: and z2 = 1– 2i. Write z122 and ž1/22 in the form a al numbers. and w are complex numbers with |2| =…

A: We have to find the following conditions according to the given information

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

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 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 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: For all complex numbers Zq,Z2 prove that |Z,+z2| <]z¡\+]z2l

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

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

Q: FIND THE ARG(Z) 0F THE FOUOWING compLEX NUMBERS

A: Solution

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

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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 , ² be the complex cube roots of unity. Let z₁, z₂, z, be complex numbers such that z₁+z₂+z3 = A…

A: We will use properties of cube root of unity  ω3=1  and  1 + ω + ω2 =0

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: For all complex numbers Z1,Z, prove that |2z|+|*z|s]°z+z[

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

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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: Let z2 = -V2 + i/3, w = -3+ 3i and p= -3– 2i. 1. Find all the complex numbers given by In z2.

A: It is given that