Evaluate the complex numbers j(3 – j4)* (-1+ j6)(2 + j)² (a) z1 1 +j 4 – j8 11/2 (b) Z2

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: (a) 2122 + 22Z3 + 2321 (b) (c) Re(z) +Im(2?

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

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: The real part of csch(1 + j2) is _____.

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Q: Explain and demonstrate the multiplication of complex conjugates using 2 + 3and its complex…

A: Given : 2+3i

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

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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: What is the multiplicative inverse of the complex mumber z = 2-5i? 2 В. 29 29 c (1) D. (;=) А. C.…

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Q: Multiply the complex numbers 15+j4 and 12+j4

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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…

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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: Write the following complex polynomials in factored form. You may check your final answer using…

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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: (a) Simplify the following () 62 (i) V-180 (b) For the complex numbers 21 = 8+ 15j and z2 =-3 + 8j,…

A: →j2 = -1→j4 =j2 × j2 = -1×-1 =1             So, j4k =1 , where k is any natural number.→Let z= x +…

Q: Express all answers in Rectangular Form. 1. (1 + j3)z² + (5 + j6)z + 7 – j6 = 0 2. 3z? – (5 – j4) z…

A: Since you post more than three subparts questions as per our guideline we can solve only first three…

Q: a. Factor the polynomial over the set of real numbers. b. Factor the polynomial over the set of…

A: 107. Given polynomial is: fx=x4+2x3+x2+8x-12 We have to factor the above polynomial over the set of…

Q: 4. Perform the following operations involving complex numbers: a. (2 + 7i) + (3 – 4i) b. (9 + 5i) -…

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Q: What is the conjugate of 3- 2/5?

A: conjugate is where we change the sign in the middle of two terms . So ,conjugate is 3+2√5

Q: Determine the conjugate of the product of, (3 – 2i) (4 + 3i)

A: solution:-3-2i4+3i=34+3i-2i4+3i=12+9i-8i-6i2putting i2=-1=12+9i-8i-6-12=12+9i-8i+6=18+i

Q: Perform the following operations on the complex numbers. a) (4– 6i) – (-8 - 9i) b) (4 – 6i)(-8 – 9i)…

A: (a) Perform the subtraction operation for the given complex numbers.…

Q: Simplify the complex power [(1+i)/(1-i)]-2i  and leave your answer in its simplest form.

A: Use the following formulae, to obtain the solution.…

Q: Prove that zª +1 = (r² + √2x+1)(x² − √√2+1). Then factor z¹+1 into linear factors over the complex…

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Q: Find the imaginary part of 23t where z = x+ iy (the denominator is the conjugate

A: The conjugate of z will be x-iy

Q: (a) Simplify i*+1 in real and imaginary parts.

A: As there are two questions given ,i only do the first.