1. Solve the equation (z+6i°)(3i° – 5i’ ) =-8(1– 4i) for the complex number z in standard form.

Q: a) Find the parametric equation of the line that passes through points S (2,-1,3) and T (-1,1,-2).…

A: We have to do the complex number problem and equation of line

Q: Find all the complex square roots of w 64(cos 30+ i sin 30"). Write the roots in polar form with 0…

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Q: The complex conjugate z is denoted as z̄. Solve for z in the equation:…

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Q: Find the complex roots of the equation z = 1 + i

A: We have to find the complex roots of the equation z5=1+i.

Q: Question 5 What are the complex solutions for z? 6r + 34?

A: According to our guidelines we are supposed to answer only the first question if you want any…

Q: z2 + (3 – 2i)z + (2 + i) = 0

A: Here, we need to solve the following complex number equation.                 z2+(3-2i)z+(2+i)=0 Let…

Q: b. Write the complex number Z = (3+ m) + i)" in polar form

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Q: Find the value of x and y in the following complex equation: 1 1 = 1 1 + 2i x + iy

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Q: Solve the following  complex numbers in their rectangular form

A: Given,             Z3Z2 Where in Z2 = 5e2i and Z3 = 4 cos 40°

Q: 30. The complex number 1 + V3i can be expressed in exponential form as 2e A в 2e- is 2e- 2e D

A: In the given question we have to expressed the complex number z in the exponential form…

Q: 2) The complex conjugate of z is denoted as z. Solve for z in the equation: z - 12 = j(9 – 2z)…

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Q: iv) in complex number z3. (7)? = |z|?. z

A: Complex number: A complex number has the form z=x+ιy, where x is called the real part and y is the…

Q: 1 d) In this thesis we consider complex numbers and in terms of the imaginary unit.   Find all…

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Q: 3 What are the solutions to x³ = -2 – 2i in polar form?

A: The complex number is x3 = - 2 -2i

Q: Find the product in the complex plane. i sin 6 + i sin 6 COS + i 6

A: Complex plane.

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

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Q: −j j sin² zdz

A: Consider I=∫-jjsin2zdz

Q: Determine all complex solutions of the equation cos(z) = 2.

A: First represent cosz in exponential form then make quadratic equations to find solutions as in next…

Q: The negative complex roots for the quartic equation x* +x² –1=0 are: 1-5 b. i + a. ti 2 c. ti 2 |1+…

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Q: ind the roots of complex numbers 1. z3 = 2 – 3i

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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: snip

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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: Solve the following complex numbers: Z1 = 5+3i ; Z2= 4+5i ; Z3 = 3-i 1.The roots of (Z3)^(1/3)

A: I am going to solve the given problem by using some simple algebra to get the required result.

Q: 3. Find the cube root of the given complex number: y= (4 – j3) i.e., find V(4 – j3)!. You may leave…

A: Given: z=4-3j To find: Cube root of a given complex number.

Q: Solve the following complex numbers: Z1 = 5+3i; Z2 = 4+5i ; Z3 = 3-i 1. The product of Z1*Z2 2. The…

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Q: Evaluate the complex number sin(0.346 – 0.548i), -

A: We know that  sin(ix) = i sinhx,   and  cos(ix) = coshx  sin(A-B) = sinA cosB - cosA sinB

Q: Show that the complex number z = −1 + i satisfies the equation z2 + 2z + 2 = 0

A: we have to show that the complex number z=-1+i satisfies the equation z2+2z+2=0

Q: find all complex values z satisfying the given equation cosh z = 2+3i

A: We know that - cosh x= (ex-e-x)/2 using it, the explanation is given below-

Q: Express the complex number z = - 1 - (square root 3)i in polar form: Z = r ( cos ( θ ) + i sin ( θ )…

A: Explained below

Q: Question 11 Find all the solutions of the equation z* – 6z² + 12 = 0, including the complex…

A: To find - Find all the solutions of the equation z4 - 6z2 + 12 = 0, including the complex solutions.

Q: ) Find the Cartesian form (i.e. æ + jy where x, y E R) for the complex number 1 (2+ j)(1 – 2j)´ - )…

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Q: (a) Express the complex number 2 + (2/3)i in the form r(cos 0 +i sin 0), -n < 0 <T. (b) Solve the…

A: Complex numbers are those numbers which is represented in the form of a + ib where is a real part…

Q: z = v3 - i, and let w = 6 (cos () + i sin COS | a.) Write z in polar form. b.) Find zw. Write your…

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Q: Find all complex numbers z E C that satisfy the equation (7) + 3 = 0.

A: Solve the following

Q: Find all the complex square roots of w= 81(cos 30° + i sin 30°). Write the roots in polar form with…

A: Solution:- Complex root of w=81cos 30°+i sin 30°   wn=rcos θ+i sin θ wk=xr cosθ+2πkn +i sin θ+2πkn…

Q: logz, (z3":) \0gz;

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Q: 2n Express the complex number z = 8 cis 4 in 3 rectangular form a + bi. Select the correct answer…

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Q: 1 If a complex number z satisfies | -3 | z+3 find the largest %3D sin75 ° cos75°* Value of | z+i|.…

A: We are given that a complex number z satisfies z-3+z+3=1sin75∘ cos75∘ . So,…

Q: Find all the complex square roots of w 9( cos 45° + i sin 45°). Write the roots in polar form with 0…

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Q: T Convert the complex number, z = 4( cos| + i sin from polar to rectangular form. Enter your answer…

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Q: Question 5 What are the complex solutions for z? 6z +34?

A: Wr can easily find given expression complex solution by using shri dharacharya method

Q: b. Write the complex number Z = ((3+ m) + i)" in polar form

A: Given: The given complex number is z=3+m+i4=7+i4. (given m=4)

Q: Let a = V3 – i and b = –1 + i be two complex numbers. (9a) Compute the value of b18 a7 = Z (9b) Find…

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Q: Solve x2 + 25 0 over the set of complex numbers. +25 15i 土5 D 125i

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Q: Transform z = 2- 4i into trigonometric, polar, and exponential form.

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Q: 2(2) A complex number z = v2(cos+i sin ), find In ( Z.Z' )

A: z = √2(cosπ/4 + i sinπ/4)  z = √2(1/√2 +i/√2 )  z = (1+i)  z* = 1-i