1. (a) If z1 = -3 - 5i and z2 = -5 – 7i are the two complex numbers, then %3D 21 + 22 + i123 21 – 22 – i14 evaluate

Q: 2. Write down the complex (a) 3+ j4, (b) 2 j. [(a) 3 -

A: See the details solution in below

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: 4.Find all complex numbers of the form z=a+bi, where a and b are real numbers such that zz = 25 and…

A: To find out all the complex numbers for the given condition.

Q: 1. Express the sum of (2 - 3i) and (6 + 4i) divided by the sum of (4 + i) and (-5- 2i) in a + bi…

A: 1)  To find the value of           {(2-3i)+(6+4i)} / {(4+i)+(-5-2i)}

Q: 1. Consider the nonzero complex numbers 21 5i z2 = 4i and z3 (z1 + z2 + 23) (a) Evaluate (z1 22 Z3)…

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Q: 1. ________ Theorem states that if z = r(cos θ + i sin θ) is a complex number and n is a positive…

A: Given: 1. ________ Theorem states that if z=rcos θ+i sin θ is a complex number and n is a positive…

Q: 1. Consider the nonzero complex numbers z1 = 3i, z2 = 6i and z3 = 4i. (a) Evaluate (z,z,z3) (1 + z2…

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Q: Let , ² be the complex cube roots of unity. Let z₁, Z₂, Z3 be complex numbers such that Z₁ + Z₂ +Z₁…

A: Given that, Let ω,ω2 be the complex cube roots of unity. Let z1,z2,z3 be complex numbers such that…

Q: 3. The complex computation (6+2i)(6–21)–(3–4i)(3+4i) can be simplified to (1) 15 (3) –10 (2) 39 (4)…

A: Given: 1) (6+2i)(6-2i)-(3-4i)(3+4i) 2) 7-i3+i

Q: 1. Simplify the complex mumbers below. i (3+ 5) + (10-14) i. (3+5) - (10 -14) i. (3+ 5)(10-14i)

A: According to the given information it is required to simplify the complex numbers given in each…

Q: 1-181 Q2- The complex number z satisfies the equation 4Z - 3Z %3D 2-1 Then

A: TO FIND: Z =

Q: if (1+i)(x+iy) = 2+4i then 5x is: * O 15 O 10 05 O 3 Let z be a complex number such that |z| = 4 and…

A: Given (1+i)(x+iy)=2+4i. We find 5x.

Q: 3. Convert the Complex number 10V3- 10i to trigonometric form: r(cos(0) + i sin(0)). 4. Let z =…

A: I have Provided this answer in step-2.

Q: Let z be a complex number with |z = 11 and let z0 = 17 – 20i. What is |z – z0| + |z+ zo|??

A: Given:- Let z be complex number with |z| =11 and z0 =17 -20i  To find:- value of |z - z0 |2 +  |z…

Q: ii) How would you describe geometrically the relationship between a nonzero complex number z = a +…

A: Given: Describe geometrically the relationship between z=a+ib anda. −zb. z−1

Q: Find in the form of red, the six complex numbers which satisfy the equation 2° +32+32( V3 )i = Hence…

A: Given:                       z6+32+323i=0 ....... (*) To find: Solution of (*) of the form reiα.…

Q: Let z be a complex number with |z|=17 and let z0=17−11i . What is |z−z0|^2+|z+z0|^2 ?

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Q: 1. Consider the nonzero complex numbers z1 = 3i, zz = 6i and z3 = 4i. (ə) Evaluate (2,2,z,) Ei++*)…

A: given Data: z1=3i, z2=7i, z3=7i

Q: 19. The modulus of the complex number 3+i. Is 2-i B. vZ C. 10 A. - 3. D.= - 4 V 3 V3-i 20. If z =,…

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Q: 6. Find the following complex numbers in the form r+ iy, whe and y are real. (i) (3+7i) + (6 – 10i)…

A: we have to find complex numbers in the form of x + i y  Adding real part with real part and…

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: 3) The complex conjugate of z is denoted as z. Solve for z in the equation: 27(1 – j2), j 2- j3 1 +…

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Q: 1. Consider the nonzero complex numbers z1 = 5i z2 = 4i and z3 = 2i (b) Find the principal value of…

A: Follow 2nd step.

Q: B. Express in the form of a complex number x+iy 1. (2+34)+(-4+5i) 2. (3+ 2i)(3 – 31) 8+4i 3. 1-i

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Q: 1. If z = 1+ iy is a complex number. Use the exponential form to compute (1+ /3 i)201

A: Definition used -            DeMoivre's theorem -             For a complex number z=r(cosθ+isinθ)…

Q: 8. Consider the complex number z = 2 + i and w = 7 – 2i. Write down the real and imaginary parts of…

A: Given : The complex numbers z = 2 + i  and w  = 7 - 2i.   To write the real and imaginary parts of…

Q: 1. Consider the complex number z = -2(1 + i). (a) Compute z' by multiplying z by itself three times.…

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Q: Let z be a complex number. Then the solution(s) of sinhz+coshz=1/e is (are) * None of these does not…

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Q: 137 COS 18 13T 4( cos +i sin ) and 37), express the result of z1 z2 in rectangular Given the complex…

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Q: If z1, Z2, Z3 are complex numbers such that |z| = |z2| = |Z3| = %3D 1 1 = 1, then |z, +z, + z,| iS

A: Introduction :

Q: 1 Let Has a general complex-valued solution, -2 1 Dje(l+2)t + Dze(l-2i)t Give the general…

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Q: 3) The complex conjugate of z is denoted as z. Solve for z in the equation: 27(1- j2) j 2-j3 1+ j2…

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Q: Q3- The complex number is defined as Z = 2 +i and given that Z - 3i + p(Z - 4i) = qZ then p .. and q…

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Q: Photo #1: Question Photo #2: Answer Key

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Q: 1-181 Q2- The complex number z satisfies the equation 42 - 37 2-4 Then

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Q: Plot the complex number. -6(1 + V31) Imaginary Imaginary axis axis 15 15 -6 (1 + v3 i) 10 10 5 5 Rea…

A: Complex numbers

Q: Let z₁,z, and z, be complex numbers such that |z₁|=|z₂|=|z₁|=|z₁+z₂+z₁|= 2. If and z₂ #z,. Then find…

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Q: Q3- The complex number is defined as Z=2+i and given that z- 3i + p(Z" - 4i) = qz then p and q ...

A: Complex number: - A complex number is one that may be represented in the form a + ib, where a, b are…

Q: 18. Let z be a complex number satisfying 12|:|* = 2|z + 2|² + |z² + 1]² + 31. What is the value of z…

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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: 3) The complex conjugate of z is denoted as z. Solve for z in the equation: 27(1- j2) j 2- j3 5z 1+…

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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 satisfying 12|z|² = 2|z + 2|² + |z² + 1|² + 31. What is the value of z +-?…

A: Given that Let z be a complex number satisfying  12z2=2z+22+z2+12+31 To find the value of z+6z

Q: 1-181 Q2- The complex number z satisfies the equation 42 - 32 2-1 Then Z =

A: Given that  The complex number z satisfies the equation 4z-3z'=(1-18i) /(2-i)

Q: (b) Calculate (i) z1 + Z2. (ii) z, Z2. (iii) z1/z2.

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Q: 1. Consider the nonzero complex numbers z1 = 5i z2 = 4i and z3 = 2i (21 + z2 + z3) (21 z2 z3) (a)

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Q: Ifz is a complex number, then sin-z can be written as (A)-i In iz+ (1-z) (B)t In [iz + (1 -z)]…

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Q: (c) 1(3-iz)리 on l리<1 (d) 15 + 2iz리 on |리 < 1

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Q: 3.1. Express each of the following complex numbers in the form x+iy: (a). (V2 – i) – i(1 – v2i),…

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