Express the result in trigonometry and rectangular form Complex Number Arithmetic Let -1 + V3i Z1 = V3 + i and z2 = Perform the indicated %3D 2 operation and express the result in both trigonometric and rectangular form. Recall that 7 denotes the complex conju- o gate of z; that is, if z = a + bi, then 7 = a – bi. %3D %3D 30. (z2)

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

A:

Q: . Define complex variable and complex conjugate with example

A: Topic = Complex number

Q: (1 + i) 201.

A: Now…

Q: Q4a. Evaluate the complex number e2+3i In(2+i) 3+4i

A:

Q: Draw f (E) in complex numbers system if f (z) = z +Z + izz and E = {z e C:1 < |z| < 3}. %3D

A: Given is a function f(z) and set E. First we let z = x+iy where x and y are real numbers. Then…

Q: Evaluate In(-3).

A: Let us consider a complex number z then it is of the form a+ib where a is real part and b is…

Q: Find all complex roots of the equation z6+z5+z4+z3+z2+z+1=0.

A: The given equation is z6+z5+z4+z3+z2+z+1=0    .....(1) We know that  z7-1=(z-1)(z6+z5+z4+z3+z2+z+1)…

Q: Let i denote the square root of-1. For the two complex numbers z = 3e and w = 6eT find z, w. Give…

A:

Q: Suppose the product z1z2 of two complex numbers is a nonzero real constant. Sho 2 kz1, where k is a…

A:

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: Show that x+iy | g+ix / = 1₁ =1, where X +iy and y+ix are complex numbers.

A: Here, let evaluate x+iyy+ix Using the absolute rule ab=|a||b|: =|x+iy||y+ix|

Q: 1. Let z and w be complex numbers. (a) Show that |1+ z w² + |z – w2 = (1+|z|?)(1+ |w/?). (b) Show…

A:

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: Determine Re(z) if z = 1145x-6512yi   Sucject: complex numbers

A: We have a complex number, z = 1145x - 6512yi We know that, In a complex number  z = a + bi  , a  is…

Q: Z₁ = (1+i)² 2 (1 - i)² 3 I

A:

Q: Simplifica cada producto.(Simplify each product.) (7-10) 7) (4i – 3)(2i + 7) 8) 3i(2i? + 4) 9) (i –…

A: Since you have posted multiple subparts, as per our policy we will answer first three subparts.…

Q: The complex numbers z, and z2 are such that z, = -2 + 2i and zz = -2– 2i. Find (a) arg z1 (b) |z21".

A: we have to find the value of the following

Q: 5. (a) Let z = (a + ai)(b+ bv3i) where a and b are positive real numbers. Without using a…

A:

Q: 1. Write the complex number 2+ iv3 in the form of reio . (2 Marks)

A: Here we first find modulus and arg then convert this into polar form