z is a complex number with |2| = 6. The triangle formed by z, z?, z° has a right %3D angle at z. Find the imaginary part of z, given that it is positive.

Q: To convert a complex number from rectangular form, z = a + bi, to polar form, z = r(cos e + i sin…

A: We fill the blank spaces as,

Q: Find the imaginary component if the complex number a + bi is raised to m if a = 9, b = 6, and m = 5.…

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Q: b) Write the following complex number in Cartesian, Polar and Exponential for VZ+ Või -1+ v3i

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

Q: Find the rectangular form of the complex number z that is given in polar form: z = 2.7(cos 1.9 +i…

A: Put x=r cosθ   and   y= r sinθ

Q: Determine the polar form of the complex number 5 – 3i. Express the angle e in degrees, where os es…

A:

Q: Given the complex number z1 12( cos +i sin ) and 13 %3D 8 8. z2 = 2( cos +i sin ), express the…

A: Given two complex numbers, z1=12cos13π8+ι sin13π8 and z2=2cos11π8+ι sin11π8 We have to express  z1z2…

Q: O Given the complex number z=x+yj, 27 If Arg (z+1) = and Arg (z – 1) = = 3 Determine z. Express your…

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Q: The modulus of the complex number z = 1- e" is A 2sin (0) B. 2 cos (e) В. C. 2 D. 1

A: We have to find the modulus of the complex number z=1-eiθ.

Q: The value Va? + b² is the of the complex number a + bi.

A: The absolute value of any real number is a real numbers itself . The general form of complex number…

Q: bi is raised to m if Find the imaginary component if the complex number a + a = 6, b = 6, and m = 7.

A: We have to find the imaginary component if the complex number a+ib is raised to m if a=6, b=6, and…

Q: Given two complex numbers z = 1+j, and w = 2 – 4j, which of the following options equals 2? w

A: We know that

Q: To convert a complex number from rectangular form,z = a + bi, to polar form, z = r(cos θ + i sin…

A: The rectangular form of a complex number is z=a+ib the polar form is z=rcosθ+isinθ

Q: Express the given complex number in polar and rectangular forms. 10.0 e 1.20j

A: We have to write polar and rectangular form of given complex number:

Q: Given two complex numbers z = 3 – 3j and w = 1 + 7j which of the following options equals

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Q: V-1, is If x1 = represented by the point A (4, -3) in the x-y plane shown below. If point B, not…

A: The correct answer is 26.2 (approx.)...see the attachment below for the detailed explanation

Q: 13. The complex number c + di is equal to (2 – 3i)². What is the value of c?

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Q: Given two complex numbers z 3-3j, and w =1+7j, %3D which of the following options equals ?

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Q: What does |w_1|= ?and what does |w_2|=?

A:

Q: (A+B)* = A† + B*, (AB)† = B* A*, (AA)† = XA*, %3D %3D where A is a complex number and AŤ indicates…

A: We have to evaluate ABC†. Given AB†=B†A† Hence, ABC†=ABC†=C†AB†USe AB†=B†A†=C†B†A†=C†B†A†

Q: Let z, and z2 be two complex roots of the equation z2 + az + b = 0. Assume that the Origin, z1, and…

A: Given  Let z₁ and z₂ be two complex roots of the equation                  z² + az + b = 0. Assume…

Q: The complex number (cos+ i sin can be expressed in the form a + bi, where a, be R, as 31. COS 27 27…

A: solution:-

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: The complex numbers z, and z2 are such that z, = -2 + 2i and zz = -2– 2i. Find (a) arg z1 (b) |z21".

A: we have to find the value of the following

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: Find a complex number for which Arg(z bar) does not equal -Arg(z).

A: For all non zero complex number we have Arg(z bar) = - Arg (z)  as if z = x+iy  which imples z¯ = x…

Q: find the trigometric form of the given complex number.  Then find the fourth power of z1 z1=-1+i

A: Given : z1 = -1 + i   .....(1)   comparing of this equation, a+bi from (1),                a = -1 ,…

Q: Find the imaginary component if the complex number a + bi is raised to m if a = 7, b = 7, and m = 6.

A:

Q: The complex numbers z1 and z2 are connected by the relation 1 21 = 22 + -. 22 If the point…

A: Let z2 = x+iy Given points z2 satisfy: x2 + y2 = a2 Equation in the given question: Hence point…

Q: Given that z is a complex number, sketch the common region shared by the following locus: |z – 2| 6

A: let z=x+iy

Q: Find the complex numbers in the form of z = a + bi such that zz*= 100 and a+b= 14. Note: answers…

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Q: .z³ = 8i

A:

Q: Given the complex number w = 4(cos 110° + i sin 110°). Compute the following, leaving your answer in…

A: formula : if then Given :

Q: From the following rectangular complex number Z-4+3i, Z-2-3i and Z,--5+2i Find the poler form?

A: Given:     z1=4+3i      z2=2-3i      z3=-5+2i For a complex number z, expressed in Cartesian form as…

Q: :If z is a complex number satisfying the equation (-1)" = =", where n e N. Show that the locus of z…

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Q: 3. Given a complex number a + bi, the value of a is called the part. part and the value of b is…

A: Give query is to give the names of 'a' and 'b'.

Q: Find all the complex cube roots of w = 8( cos 270° + i sin 270°). Write the roots in polar form with…

A:

Q: Find the square root of the complex number, calculate the magnitude of the number and its square…

A: Consider the complex number 3+4i. Find the square root of complex number.   let the square root of…

Q: Given the complex number z -1-V3i, find 2. Write an exact answer in polar form with 050<2.

A:

Q: Find the midpoint of the line segment joining the points corresponding to the complex numbers in the…

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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: : If z is a complex number satisfying the equation (=-1) = =", where ne N. Show that the locus of z…

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Q: If Z is complex number e? = e*(cos y + isin y) True O False

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Q: Suppose a complex number z satisfies the equation (1+ 2z)³ = eiª (1 – 22)³, for some a E (T, 27).…

A: Given equation is 1+2z3=eiα1-2z3 where α∈π,2π

Q: What are all the cube roots of -1 in the complex plane? Mutiple choice options: 1 -1 e(5π / 3 i)…

A: Given problem:- What are all the cube roots of -1 in the complex plane?   Mutiple choice options:…

Q: Which of the following provides the rectangular form of a complex number? A z=a+ bi B z=r (cos theta…

A:

Q: In the polar form of a complex number,r(cos θ + i sin θ), r is called the__________ and θ is called…

A: Given:Polar form of complex numberrcosθ +i sinθ

Q: Given the complex numbers z = V2 + v2i, find the polar form.

A: We have to write the polar form.