Show all steps to prove the complex identity. 1. Show that (a+ bi) = (a+b)(a – b) + 2abi %3D

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: 5.) Find the complex cube roots of: 8(cos 60° +i sin 60°). (write them allI)

A: We use De moivre's theorem

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

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

A:

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: 10. Find a complex number z such that (a) z – z+7 – 6i = 0 - | (b) = 3 + 4i %3D 1+ z

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

A: To find the value of 5x:

Q: a) w=−√3−3i    evaluate (−√3−3i)^15 (that would mean writing w^15 in the a+bi form)

A: Express in polar form, as follows:

Q: * Enpress the following complex #s into real and Fmaginary part 3 = It i

A:

Q: 1. If z = 1+ iy is a complex number. Find the principal argument and exponential form of z =

A: Given that z=x+iy is a complex number. where, Real Part = x and Imaginary Part= y Now,  z=i1+i…

Q: Determine the value of k such that z = 2.03 + 1.39i be a solution of the equation: iz? + z – k = 0 k…

A: If z=a+bi be a complex number then , z2 =z.z =a2-b2+2abi.

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: O Find all the complex roots of (-1 – 7i)/' 1/7

A: As per our guidelines, we are supposed to solve only first question.

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: (a) Given complex numbers, z, =-/3+ 2i and z, =-/2i. (i) Express z, and z, in exponential form.

A: Exponential form of the Complex number

Q: M 9 3 Find formulas for the entries of M", where n is a positive integer. (Your formulas should not…

A:

Q: Let z = -4 + 3i and zw = -7 – 2i. By showing clear steps, find w in the form of a+bi.

A: Given:        z=−4+3i,  zw=−7−2i

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: Express the following complex number in exponential form: (3 - 4) O -V5e-5.36/ 5e5.361 5e-5.36i…

A:

Q: Write the complex number z=(1-√3i)2015/(√2cis(7π/6))4028 in an exponential form.

A: cis(x) = cos(x)+isin(x)

Q: Find the real component if the nth root of a + bi is determined for a = 10, b = 9, and n = 7. Round…

A: Given  a= 10 b=9  a+bi=10+9i n=7

Q: For every real number a > 0.Find all the complex numbers z which satisfy hte equation |zf- 2iz + 2a…

A: Solution is given below:

Q: A complex number z satisfies arg z = 5. (a) Use a diagram to show that |z-2i| > 1. (b) For which…

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Q: 5) A = 2i+3j+5k and B = 3i+6k, Determine the direct cosine of (AXB). %3D %3D

A: Finding the cross product of vector A and vector B  i×i=j×j=k×k=0, i×j=k, j×k=i, k×i=j, j×i=-k,…

Q: Which of the following expresses the complex number z = 2Z in rec O z= 2+ 2j O z = V2(1 + j) O z=…

A: We have to find

Q: Evaluate the complex integral 033.png 2+3i az 2p- bz? +c if a = 9.3, b = 3, and c = 12. Then, find…

A:

Q: . Let z = -4 + 3i and zw = -7 – 2i. By showing clear steps, find w in the form of a+bi.

A: In this question , the value of z is inserted into zw=-7-2i, and then it is solved for value of w.

Q: Recall that the complex conjugate of a = a + bi E C is a = a - bi. Show that aßaß for every a, B e…

A: Given;  Alpha = a +b i.

Q: Given the complex numbers z = 2 + j3,zz = -1 - j2,andzg=4+j4 find; Im (高)x+x@zs)+Im(zz+z) (元)

A: Given: Complex numbers are z1=2+j3, z2=-1-j2 and z3=4+j4. To find:…

Q: Given the complex numbers z1 = -3+i and z2 :1+4i. Show that %3| |z1 22| = |21||2| and arg (z1 22)…

A: |z1|=√(x2+y2) use this formula prove that |z1z2|=|z1||z2|

Q: - Find the roots of the following complex nos. 3. %3D 3. Z =\ Z-27-0 %3D 3. |

A:

Q: If |x = 3i| <5, then prove that the complex number z also satisfies the inequality i(z+1)+1| <25.

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Q: The expression 3 + 4i is a complex number. Compute the modulus of complex number. a. 4 b. 5 c. 6…

A: Given complex number is 3+4i. We compute the modulus of this complex number.

Q: z + 2i = iz + A, " = 2+ 2i, Imw = 8, where z and w are complex numbers, and A is a real constant.…

A:

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: What is the exponential form of the complex number 4 + 3i A) 5eba, 13 B) 5ebs,a7e © 7e5z, 12 D 7e…

A:

Q: z = 1 + √3i

A: Z=1+3imodulus of z is z=12+32                         z=1+3                          r=z=2

Q: Given that Z1 =1– 2i, z2 = -3+4i. Find and express it in a +bi Z2 form.

A: As per our guidelines, we are allowed to answer only one question. Since you have asked multiple…

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: Use Bombelli's approach to find a complex number c = a + bi such that = 18 + 26i where a and b are…

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Q: 15. Match each expression on the left to its complex form a + bi on the right. 1. -V-64+8 а. —3 + 3і…

A: We have to match expressions to their complex form.

Q: Let 1 M = 1 Find formulas for the entries of M", wheren is a positive integer. (Your formulas should…

A: The given matrix is M=1-771. To find the higher power of the matrix, we need to diagonalize the…

Q: (a) Given complex numbers, z, =-V3+2i and z, =-/ /2i. (i) Express z, and z, in exponential form.…

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

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Q: 1. Find modZ and argZ for the complex numbers given below. 1+1/2 Z = 1-V7

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Q: (a) The complex conjugate of 3 + 4i is 3 + 4i (b) (3 + 4i)(3 + 4i)

A: (a) For a complex number a+ib,  a+ib=a-ib So  3+4i=3-4i

Q: 4. a) Given that z = 2 – 3i, express i'z, and Z/Z* and Z (cos - isin -) in the form a + bi, where a…

A: