1. Consider the nonzero complex numbers z1 = 3i, zz = 6i and z3 = 4i. (ə) Evaluate (2,2,z,) Ei++*) (a) Evaluate (z1zz3) (31 + z2 - z3) (b) Find the principal value of (z1z2z3)

Q: Simplify the complex number (Z^3) * ?and find the Re(z) & Im(z)

A: From De Moivre's Theorem we have,  Let z=rcosθ +isinθis a complex number in polar form. If n is a…

Q: Q2\ If z = 1 + i, what is z3 + z? + z + 1 as a single complex number?

A: Use the following formulae, to simplify the given expression.…

Q: 3. (a) The complex conjugate of 3  4i is 3  4i  .(b) 13  4i2 13  4i2  .

A: a) Complex conjugate of 3+4i is, By definition, For a complex number z=x+yi, its complex conjugate…

Q: Suppose the complex numbers x and y satisfy the following equations: xy - y² xy + 2x² = = 3 1 (A) 8…

A: Answer is D. 16

Q: iree complex Z1 = 1- 2i, z2 = 6i, z2 = -3 -i. Compute the following, with your answer expressed in…

A: given that z1=1-2i,z2=6i,z3=-3-i find a)z1+z2z3b)3z2*-4z1z1c)z1z2*-3iz3

Q: 21-5 1. a) Convert the complex number to the form a + bi. 1-3i 1. b) P(x) = x* – 3x' +5x² - 2 What…

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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: Q1) Find modZ and ArgZ for the complex numbers given below: 1+i√2 1-i√2 2 2+i a) Z= b) Z= +2-i

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: 2.2 Simplify the complex power ()-“ and leave your answer in its simplest form.

A: Given 1+i1-i-2i

Q: Verify that (¹)² = i²i but that (i²)i ‡ į²i ("i" imaginary unit)

A: What is Complex Number: A real number and an imaginary number are effectively combined to create a…

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: 4Q Express 2= (1+2i)² 7-i in the form a + ib where a and b are real numbers.

A:

Q: iii) How are the complex numbers z1 and zz related if arg(z1) = arg(z2)? Buildup examples for this…

A: Given: z1,z2 are two complex numbers such that argz1=argz2, To find: The relation between z1 and z2,…

Q: Find the complex conjugate of (2+3i)/(1-i)

A: We find complex conjugate of (2+3i)/(1-i)

Q: Write the standard form of the complex number 4(cos(4π÷3)+isin(4π÷3)    Find the product:…

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Q: [-3i-2]]-[-2i-5j]= • 2 + ງ

A: Given-3i→-2j→--2i→-5j→

Q: What is the result of multiplication of complex numbers -√3+1 and (cos+ i sin )? A (cos+isin) B (cos…

A:

Q: 2. Write the given complex numbers in the form a + bi. 3 (a) 를 + 을-2유 (b) 2,0 + + 5i 5- 12i (c) 2-4i…

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Q: Simplify the complex number 7 (²+1) ³ - 5 (¹)² and express it in the standard form.

A:

Q: If the complex number z and its conjugate z' satisfy zz' + 2(z - z') = 12 + 8i, then the values of z…

A: Explanation of the answer is as follows