(5- j6) - (2- j8) (-3 + j4)(5 – j) + (4 – j6) Given a complex number z = - Its magnitude is and its phase is (degress)

Q: 3- where a is a complex number 1³ + axy² + 1 + iv(r,y) dz 22 |z|=1

A: Let the function fz be analytic on and inside a positively oriented simple closed contour C and z is…

Q: 1-181 Q2- The complex number z satisfies the equation 4Z - 32 %3D 2-1 Then Z =…

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Q: 3+2 сos @ de 5+ 4 cos 0

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Q: Plot the complex number. 3 + V3i Imaginary Imaginary axis axis 4| 4| 2 2 Real Real -4 -2 4 axis -4…

A: To plot the given complex number

Q: (a) (i) Use de Moivre's theorem to evaluate v-15 – 4i in two decimal places. (ii) Given that z is a…

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Q: iree complex Z1 = 1- 2i, z2 = 6i, z2 = -3 -i. Compute the following, with your answer expressed in…

A: given that z1=1-2i,z2=6i,z3=-3-i find a)z1+z2z3b)3z2*-4z1z1c)z1z2*-3iz3

Q: 1) Plot z = -2 + 5 i in the complex plane and find its absolute value #2) Plot z = 3-4i in the…

A: Given: To Plot a) z= -2+5i b) z= 3-4i c)z= 4-6j d) z= 5-12j Let horizontal axis be real axis and…

Q: Two complex numbers z1 and z2 are given by z1 = 3 + 2i and z2 = − 1 − 4i. Evaluate, (a) |z1z2| (b)…

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Q: y" - 2y' + 6y = 0

A: Given the differential equation is y'' - 2y' + 6y = 0

Q: The complex number Z1and Z2 are given by, Z1 = 3 – 5i and Z2 = -1+ 4i Determine: 2Z1 +5Z2

A: We have to determine 2Z1+5Z2 for the given complex numbers: Z1=3-5i and Z2=-1+4i Finding 2Z1:…

Q: Let z be a complex number. Then i(cosh(3z) + sinh(3z)) a, ie3z b. ie-3z с. е 3г

A: The given expression is icosh3z+sinh3z where z is a complex number.

Q: iii) modulus of complex z = e"H equal to а. 3 b.2 С. 1 d. 0

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Q: If the complex number z = x + iy satisfies the condition |3z - 6i| = 3, then z lies on a. Circle…

A: We know that z=x+iy and z = x2+y2 Then 3z-6i = 33(x+iy)-6i = 33x+3iy-6i = 33x+(3y-6)i =…

Q: . Two complex numbers a + ib and e + id are equal if and only if a - c and b - d. Use this fact to…

A: Given :             ∫ ea+ibx dx = a-iba2+b2 e(a+ib)x + Cwhere C = C1 + C2  is a complex constant of…

Q: 1-18 Q2- The complex number z satisfies the equation 4Z - 32 2-1 Then Z =

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Q: Q2- The complex number z satisfies the equation 4Z- 32 %3D 2-1 1-181 Then Z = ......... ..*......

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Q: 8e2i 5e-0.7i Express the complex number p= to a rectangular form. Determine the quotient of in…

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Q: How may the following complex numbers be obtained fromz = x + iy geometrically? Sketch. -z

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Q: Q3) Find complex root of the z³ = -27, k = 0,1

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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: Plot the complex numbers –2+i and 8 –3i in the complex plane. Imaginary Axis 8. 6- 4. 3. 2. Real…

A: see below the answer

Q: 8. x" – 1 = 0, when x is complex 9. x" + 1 = 0, when x is complex 10. X - 10. х — ах + b 3 .3 = 0.…

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Q: Find the distance between the points 2+3i and 5 -2i in the complex plane. (Round your answer two…

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Q: 2Q: Express the complex number z = -2√√4 +11i in polar form and also represent it graphically. Hence…

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Q: iii) How are the complex numbers z1 and zz related if arg(z1) = arg(z2)? Buildup examples for this…

A: Given: z1,z2 are two complex numbers such that argz1=argz2, To find: The relation between z1 and z2,…

Q: %24 Express -64- V-49 as a complex number (in terms of i): V-64--49 = > Next Question SEP 30 MacBook…

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Q: i) Find real and imaginary part of complex number (V3 + i)° by using De Moivre's Theorem.

A: Consider the complex number: 3+i3 Comparing the complex number 3+i with standard form of complex…

Q: (b) Shade the region in the complex plane defined by z+1+i 2-1-5i

A: Solution:-

Q: The real part of the complex number z = (2+2i)² + e¹+2i is

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Q: 1. For the complex numbers: 21 = v2 – i, z2 = 1 – iv2. Find the polar and exponential form of the…

A: given: z1=2-i z2=1-i2 we have to find the polar form and exponential form of the complex number…

Q: Find the value of y in the complex equation (2x-3yi(3 + 4i) 78-21i O5 -3 03 -4

A: Given, (2x-3yi)(3+4i)=78-21i Expanding the LHS⇒ (2x-3yi)(3+4i)=6x+8xi-9yi-12yi2…

Q: Plot the complex number on the complex plane and write it in polar form and in exponential form.…

A: Find the polar form and exponential form of a complex number

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: 1. Use Cauchy - Reimann Equations to identify if it is differentiable or not, if yes then…

A: Cauchy Reimann eqaution: Let f(z)=u(x,y)+iv(x,y) be a function then  ∂u∂x=∂v∂y∂v∂x=-∂u∂y If the…

Q: Two forces are acting on a point. The first force has a horizontal component of 5 newtons and a…

A: Let the two forces acting on a point is F1 and F2. Given,  F1 has a horizontal component 5 N and…

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

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Q: Express the complex number -2e z =V2e :3T in algebraical form z=x+iy x=-iv2, y = iv2 x =-1, y =1 x…

A: Hence option (c) is correct.

Q: What is the shape of the graph of the equation z +z = 4 in the complex plane? A vertical line A…

A: In this question, concept of complex number is applied. Complex Number A complex number is denoted…

Q: Plot the complex number. 3 - V3i Imaginary Imaginary axis axis 4 2 3 - V3 2 Real Real -2 2 4 axis -4…

A: Here if you take Real axis as vertical axis and imaginary axis as horizontal axis then only option 4…

Q: Q3 Put the complex number Z = 18 + 26i in the "polar" form Z = rele where r, 0 ER and both r and 0…

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Q: The complex number z=2eiπ/4 can also be written as z=√2i z=√2+√2i z=2+2i z=√2

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Q: 1-18i Q2- The complex number zsatisfies the equation 4Z - 37 2-i Then Z = ......... .........

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Q: i Given two complex numbers zı = -6 – 3i and z2 = 4 – 7i. Express in the form of x + yi where x and…

A: We have to solve given problems:

Q: Complex number z= (4+i)/4-i 1. How can you express the equation above into its polar form? 2. How…

A: z=4+i4-i

Q: b) Integrate the above via partial frachion decomposition 6ver the complex numbers" X= - b b2-4ac X…

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Q: Q2- The complex number z satisfies the equation 4Z-32 Then ........ .............

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Q: If the complex number z = x + iy is a solution of the equation z2 + z + 1 = 0 then show that z = x…

A: z2 + z + 1 = 0 Solve the given equation using quadratic formula…

Q: what is the phase in degrees (with respect to the +x axis) when dividing two complex numbers, Z1/Z2?…

A: We have to find the phase in degrees when dividing two complex numbers Z1/Z2 . Where ,…