(A) Simplify the complex number z and express it both in rectangular and polar form. (3 + j6)(6+ j4) +7+ jl0 (2+ jl)j2

Q: (a) For complex numbers z₁ = 6 + 6j and z₂ = 4 − 4j, π (i) find z = 21. Present your result in polar…

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Q: Let z is a complex number and Z is the conjugate number of z then () equals O a. z1 Z2 b. 21 Z2 C. O…

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Q: 4.Find all complex numbers of the form z=a+bi, where a and b are real numbers such that zz = 25 and…

A: To find out all the complex numbers for the given condition.

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: Determine the four fourth roots of the complex number Z 3-4j, using De Moivre's theorem and express…

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Q: The conjugate of complex number z satisf y: Z-Z=2ilmz O z+z=10 z+z=2Rez O

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Q: 1. Consider the nonzero complex numbers z1 = 3i, zz = 6i and z3 = 4i. (ə) Evaluate (2,2,z,) Ei++*)…

A: given Data: z1=3i, z2=7i, z3=7i

Q: 1. Simplify the expression r-q+p ª × (ªª) ²¯¯** × (ª)¹-¹*¹. (at)a-p+² p-r+q 2. Represent the polar…

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Q: 2Q Express the complex number 1+ 3i in the form x + yi, where x and y are real numbers. 1-2i

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Q: Q1/ Plot the complex number z-V3 +i in the complex plane and then write it in its polar form.

A: The given complex number is z=-3+i

Q: Applying De Moivre 's theorem in writing the complex number (-1-i)* in the form a + bi, the value of…

A: Given. We need to simply the complex number (-1-i)⁸ usi de moivres theoram. De moivers theoram…

Q: b) Prove complex numbers z1=3/2z-315° and z2=3+j3 are equal. c) For complex numbers z1= 10260° and…

A: Topic = Complex number  As per guidelines,  only three sub-parts of a question can be answered.…

Q: The conjugate of complex number z satisfy: z+z=2Rez O Z-N=2ilmz O z+z=10

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

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Q: 11a Express the complex number z 10 cis in 6. rectangular form a + bi.

A: Given problem is :

Q: (-5j)" – j(j+3)(j–2) 4j-3 a) Find the real and imaginary parts of complex number z = Present this…

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Q: Simplify the complex number z and express it both in rectangular and polar (A) .form (3 + j6)(6+ j4)…

A: Now, we have to simplify the given complex number and express it in rectangular and polar form.  The…

Q: If z and z are conjugate complex numbers, find two complex numbers, z = : = z; and z = z,, that…

A: Note some result about complex number : Suppose z is a complex number then there exist a,b∈ℝ such…

Q: e the complex number 8e" in a + bi form X error - invalid form

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Q: 1. Consider the complex number z = -2(1 + i). (a) Compute z' by multiplying z by itself three times.…

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

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: Plot the number -2 – i on the complex plane. 4- imaginary real -4 -3 -2 -1 -1 2 3 4 -2 -3 -4 32

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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: (A) Simplify the complex number z and express it both in rectangular and polar form. (3+ j6)(6+ j4)…

A: Given that z=3+j66+j42+j1j2+7+j10 express it In rectangular form and polar form

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: Represent in polar form and graph in the complex plane as 4. -5 V2 + i/3 5. -V8 - 2i/3 V3 - 10i 6.…

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Q: 1. Plot the complex number on the complex plane and write it in polar form and in exponential form.…

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Q: Find the location of z = -3-4i on the complex plane and find |z|.

A: The given complex number is z=-3-4i Compare with,

Q: 3. Having two complex numbers z1 & z2, with product z,z2 being real and non-zero, verify if there…

A: Answer is following .

Q: b) Convert the following complex numbers (rectangular form) to polar form i) z=5+ jl0 ii) z= 10- j21…

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Q: 3 3 3+4+16+ z = (2√3-4i) + (-√3+5i).. find polar form of the complex number

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Q: Let z be a complex number such that z, z3 and z5 form an equilateral triangle on the complex plane.…

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Q: 3n i Let z = V2 e 4. Write the complex number 1/z + 2° in normal form (in the form a + ib).

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Q: 4i Rewrite the complex number 10e“ in a + bi form a b = II

A: We have to write the complex number 10e4i in a + bi form.

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

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Q: - find polar form of the complex number z = (2√3-4i) + (-√3+51)..

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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: The complex number z is given by Z = z²+1 a²-b² 2z a² + b² a+bi a-bi show clearly that

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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: 10 + j5 +3440° - 3+ j4 Evaluate this complex number: +10230° and represent it in the polar form,…

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

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

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Q: Find all points on the complex plane which represent the complex numbers w = (V3- 1)z+1-2i, given by…

A: We know that, z=2eiϕ, ∀ϕ∈ℝ implies the circle of radius 2 with center at origin. Graphically: Now,…

Q: Let z₁ = 5+2i, Z₂=1+3i, z3=2-3i, Z4--4-7i. (a) Plot the complex numbers z₁, Z2, Z3, Z4 on an Argand…

A: Solution

Q: (c) Let z be a complex number such that z, z³ and z5 form an equilateral triangle on the complex…

A: Let z be a complex number such that z, z3, z5 form an equilateral triangle on the complex plane.We…

Q: Express the complex number z = 8 cis 300° in rectangular form a + bi. Select the correct answer…

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Q: Express the complex number z = 8 cis 300° in rectangular form a + bi. Select the correct answer…

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Q: 3ri Let z V2e. Express the complex number 1/z + 2° in the form a + ib.

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