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

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

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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 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

A:

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

A:

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

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Q: If a2 1,Find all complex numbers z which satisfy the equaution z +a| z +1+i=0.

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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(z?)= 2Logz for all complex numbers O rosArg(z)st…

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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: 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(32)-i is unbounded in C. * False True

A: use:- cos(x+iy)=cosxcoshy−isinxsinhy

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: 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: If z=3-4i then express these following complex numbers in the form of a+ib: (a) (=+1)(=+i) 2z (b)

A: If z = a + ib and w = c + id then z+w = (a+ib) + (c+id)       = (a+c) + i(b+d)

Q: 1) If we have the following complex numbers: Z, =2+3i, Z, =3-2i %3D Z, (d) Find (a) Z, + Z2 (b) Z,…

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Q: (a) Given complex numbers, z, =-/3+ 2i and z, =-/2i. (i) Express z, and z, in exponential form.

A: Exponential form of the Complex number

Q: If 5 and 2 are complex numbers, then prove: (a) l-k|| (b) (c) +s|s|+|=|

A: I have solution for (a), and (b) a ..

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: 3. If z, and zz are two complex numbers, prove that

A: Let's find.

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…

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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: Let a be a complex number with 0 < |a| < 1. Then the set |z – al < |1 – āz| is: (a) a square with…

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Q: Let z be a non-zero complex number. Then Log(z?) = 2Logz O if -nSArg(z)s0 O None of these O if…

A: Explained below

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: z=x+i y geometricaly ?

A: Given: a) z¯ b) -z c) 1z To find: The complex number obtained from geometrically.

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: C. Find all complex numbers z of the form 2=x+y such that that zz = 25 and *+y = 7.

A:

Q: Let 2₁ and 22 be two arbitrary complex numbers and let C be a Denote by zi and 22 the symmetric…

A: Here two complex numbers are given in the question and a circle is given. z1* and z2* be the…

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: 17. The argument of the complex number z. where com CO is 1- i 13

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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: Given the complex numbers z1 = -3+i and z2 = 1+ 4i. Show that |z1 z2 = |z1||22| and org (z1 2) = arg…

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

A:

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: If Z is complex number e? = e*(cos y + isin y) True O False

A:

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 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: It is given that W = 2+ 2i, z + 2i = iz + X, Imw = 8, where z and w are complex numbers, and is a…

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Q: (a) Given complex numbers, z, =-V3+2i and z, =-/ /2i. (i) Express z, and z, in exponential form.…

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Q: Let z be a complex number. Then e32+ is bounded over the set of complex numbers. a. True b. False

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Q: a) Express the complex number Z 10 (cos 150° +i sin 150° ) in rectangular and exponential form. V3…

A: (a)z=10(cos 150°+i sin 150)where r=10and θ=150*π180=56πExponential form is z=reiθz=10ei5π/6In…

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 complex number. Then cos(tz)+3i is unbounded in C. * False True

A: