Let z be a non-zero complex number. Then Log(z²) = 2Logz ) None of these O if OSArg(z)ST/2 O if -nSArg(z)<0 O if OSArg(z)SrT O for all complex numbers

Q: 1. Prove that multiplication of complex numbers is associative.

A: We know that a complex number in the form of a+ib  i.e. z= x+iy =(x,y) where x and y are real…

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: What is the additive inverse of the complex number 3-7?

A:

Q: Find one or more values of each of the following complex expressions

A: We need to compute the value of the given expression.          e2tanh-1i

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

A:

Q: Let zand w be complex numbers with the following properties. |z| = 7, |w|= 3, Arg(z) = − and Arg(w)…

A:

Q: A complex numbers is a symbol x + jy, where x and y are = -1. numbers and i^2 rational O real O…

A:

Q: Let -6 M-[d] = Find formulas for the entries of M", where n is a positive integer (Your formulas…

A: The given problem is to find the matrix Mn for the given matrix M. Given matrix, M = [-6 -5 ; 5 -6].

Q: Determine all the roots of z +1 = 0

A: The given question is related with complex analysis. We have to determine all the roots of z4 + 1 =…

Q: Find the modulus and argument of the com

A: Given,          7-xi5+3i2 and  x = 2.

Q: Determine all complex numbers that satisfy the following identity: log (:) = - log(2) ?

A: We have to solve given problem: Given identity:log1z=-logz…

Q: Find the modulus and argument of the following complex number. z= (3+2j) (- 1+2j), giving the…

A:

Q: 4 Get all the roots of 2(V3i – 1) |

A:

Q: Let M = · [677] Find formulas for the entries of M", where n is a positive integer. (Your formulas…

A:

Q: Prove that multiplication of complex numbers is associative.

A:

Q: The set of all complex numbers is denoted by C={x+iy:x,y€R}

A: A complex number is the combination of real and imaginary number in the form of x+iy , x, y are real…

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: 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: 7. Express the complex number 1/(1+ jV3) in the form Aejº

A:

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: Which are the five roots of 1 in the complex domain? What are their natural logarithms?

A:

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

A: See solution below

Q: #2. If 2₁ and 2₂ are two complex numbers, show that 12₁-221² + 12₁ +221² = 2 ( 1211² + 122 1²).

A: 2. Let z1 = a + bi and z2 = c + di be two complex numbers.      Then,          |z1|2 = a2 + b2…

Q: 4. Show that any complex number of norm 1 (except -1) can be written in the form z = (1 + it)/(1 −…

A: We have to prove that any complex number of norm 1 (except -1) can be written in the form…

Q: Let z be a non-zero complex number. Then Log(z²) = 2Logz

A:

Q: a

A:

Q: Assuming either 121=1 Prove that Z-W 1-ZW or /w/=1 and Zw=1. = 1.

A:

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

A: