Find the conjugate of z if z = (1+ 3i) + (-2-4i) O -1+i O-1-i 01+i 01- i

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

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Q: b) Find all complex numbers z such that z= V-7+ 24i

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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: 5. Expressed in a + bi form, is equivalent to 3+1 1)- 2- 3)- i 4) 15- 5i -5i

A: Given : 53+i

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

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Q: Find all (real or complex) numbers z1 and z2 such that Z1+zz=2+4i Z1z2=-10–20i

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Q: [3-5i 2+ 4i] ++ 7i 1+8il find the conjugate of its transpose. Given A =

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Q: . Find Im(2z+4z-4i), in which ž is the conjugate of z.

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Q: express z1z2 and z1/z2 in the form a+ib. Q. z1 =1+i, z2 =3+2i.

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Q: + Zn = Z + Zz++ Zn ... 1. Prove: If z1, z2, ., Zn are complex numbers, then z, + z2 +

A: For any two complex numbers z, w; the conjugate is distributive over additio, subtraction,…

Q: Given that 2z-iz = 3(3-5/)where z denotes the complex conjugate of z a+ib. The value of a is and and…

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Q: Find the complex conjugate z¡ of z1 = –7i + 6. Z1 = %3D

A: conjugate of a function means change the sign of i term

Q: Find the conjugate of z = -2 – 4i, and compute zz. z = zz =

A: Given that: z=-2-4i

Q: The modulus of 5 + 4i is * -41 -√41 √41 41 The conjugate of (i-i² )³ is -2-2i O 2+2i -2+2i Oi-1

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Q: (b) Use Gaussian Elimination to solve: X1 - 2 x2 - X3 + 3x4 = 4 2x1 + X2 + X3- 4x4 3 3x1 - X2 2x3 +…

A: Apply gaussian Elimination to the augmented matrix and back substituting.

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: Z1 = 3 + 4i Z2 = 5 – 31i Z3 = 8+ 2i Reduce to a + bi form 1. z1 + Z2 + Z3 2. Z1 * Z2 Z1 * Z2 Z3 3. –…

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Q: Exercise 1: Given that Z1 = 1– 2i, z, =-3+ 4i. Find Z1 and express it in a+bi Z2 form. 2: 1 Given z1…

A: we are given some complex numbers. as per our guidelines we can answer only first question or first…

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: Find the complex conjugate z of z1 = -2+ 8i. %3D %3D

A: We have to find the complex conjugate {\displaystyle {\overline {z}}}1 of  z1 = -2 + 8i

Q: 3) If z =2+i, =2-3i, z, =1-i, find in the form a+bi: a. z(z, +z,) b. 2,7, +72, (Note: Z, means the…

A: z1=2+i, z2=2-3i,z3=1-ia) z1z2+z3b) z1z2⏜+z1⏜z2c) 1z2+1z3

Q: Find the complex conjugate z1 of z1 = -2i + 7. Z1 = %3D tch a video or use a hint.

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Q: If Z = 2 + 5i, write down the conjugate of Z. Multiply Z by its conjugate and write answer in the…

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Q: express z1z2 and z1/z2 in the form a+ib. Q. z1 =1−2i, z2 =3+4i

A: Given:

Q: Express z =1/(2+5i) in the form a+ib.

A: Given:

Q: If z1 = -4 - j5, z2 = -3 + j2 , and z3 = 2 - j3 , what is Re ( ? Note: z* is the complex conjugate…

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Q: express z1z2 and (z1/z2) in the form a+ib z1=-1+3i, z2=2-i

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Q: Find the real numbers x and y if (x – iy) (3 + 5i) is the conjugate of –6 – 24i.

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Q: Given that z = cos + isin and u-iv-(1+z)(1-22). Show that 30 v = utan 2 r = 4² cos² (2). where r is…

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Q: 3. (a) Show that, for any complex number z, zz = |z|², z + z = 2Re(z) and Re(z) < |z]. Hence show…

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Q: If Z=1/√2+i/√2 then the value of conjugate of Z^5= ؟

A: We have z=12+i2 Now, a complex number z=a+ib can be written in polar form as: z=a+ib=rcosθ+i sinθ…

Q: Find the complex representation of H((-1,3),3)a, where a is the translation through i = (3, –4)

A: Given: The complex representation of H(-1,3),3), Where through

Q: 1. Consider the nonzero complex numbers z, = 2i, zz = 8i and z; = 7i. (a) Evaluate (z,z,z,) (2) +2,…

A: Introduction: In most cases, the primary value Arg(z) of a complex number z=x+iy is equal…

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: 4) Let z= 1+ V 3 i. Compute all values of z". Exponential notation is sufficient. Sketch these…

A: Given: z=1+3i

Q: [3 – 5i 2+41. L6 + 7i 1+8i! find the conjugate of its transpose. Given A =

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: 6- The Conjugate of 4+3i =-(4+3i)

A: The objective is to find the conjugate of (4+3i).

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

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Q: 10. Use i = (0, 1) and y = (y, 0) to verify that -(iy) = (-i)y. Thus show that the addi- tive…

A: i=0 ,1y=y ,0 verify :   -iy = -iy  To find additive inverse of z=x+iy

Q: 1. Consider the nonzero complex numbers ž1 = 7i, 22 = 8i and z3 = 8i. (21 + z2 + z3) (a) Evaluate…

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Q: Find the quotient zi lza in standard form. 2= 3-3i, 22=1-i

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Q: express z1z2 and z1/z2 in the form a+ib. Q. z1 =4−i, z2 =1+3i

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Q: Find the complex conjugate z of z1 = -1+5i. %3D

A: Given that z1=-1+5i find the complex conjugate

Q: Find the distance d between 21 1 = (-7- 6i) and %3D z2 = (-15 – 12i). %3D

A: z1=-7-6iz2=-15-12i We can say that the co-ordinates of two points are (-7,-6) &amp; (-15,-12).…

Q: L Find the projection of i= i-2j- 2k onto = 6i +3j + 2k. %3D

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Q: Find a complex number z=a+bi such that z*z_1=1. Also, convert z into its three (3) other forms.…

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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: show work

A: The given expression is 2-1+2i

Q: Let z be a complex number such that Iz| = 4 and arg(z) = 5T/6, then z = (a) -2v3 + 2i (b) 2v3 + 2i…

A: Recall:    Let z=x+iy be an complex number then             z=r(cosθ +i sinθ)…

Q: u^2 + 2u +1 = -72 - 54i

A: Given : u2+2u+1=-72-54i ⇒u+12=-72-54i⇒u+1=-72-54i⇒u=-1+-72-54i             1