16.(Honors Class Only)Rewrite each of the following expressions involving complex numbers in the forma +ib where a and b are real numbers a) (3 +2i) (2- 5i) b.(5 +4i) (17- 13i) - (5 +3i) (17- 13i) c) ( 5/2 + 7i/2)^2 - (5/2 + i/2)^2 d (1 +i)( 13 -4i) (1- i) e) I+ i+ i^2 + i^3

Q: For the complex numbers • w = 3-5 i • z = -4+7 i Enter exact value of the imaginary part of their…

A: Product of two complex numbers (a+ib)(c+id)=ac-bd+i(ad+bc)

Q: Evaluate the sum and express your answer in Cartesian (rectangular) form of the complex number

A: Given- ∑n=0∞ejnπ2  To find- Evaluate the sum and express your answer in Cartesian (rectangular) form…

Q: 10 2) z = (-j)()

A: We have to use De Moivre's theorem cosθ+jsinθn=cosnθ+jsinnθ and Eular form of complex number…

Q: 3 – 5i - Write as a complex number. In other 2+ 3i words, find real numbers a and b such that 3 – 5i…

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Q: What happens when a complex number is multiplied by its conjugate? It turns into a real number…

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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) If z is a complex number such that z =8i, write z in the form a +bi. Given that =, =2 b where a…

A: These are complicated & lengthy problems,so I can do it in Advanced mathematics.

Q: Simplify, then express each in complex number form “a+bi” 1) -3(4+2i) -2(5-3i) 2) (4+3i)^2 3) 11+2i…

A: Since you have asked multiple question, we will solve the first 3 question for you as per our guide…

Q: 3. If a=4-i and b=10+3i, then which of the following is the value of 3a-4b? -28+9i -21-15i…

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Q: Two complex numbers are represented by c + di and , where c, d, e, and f are positive real numbers.…

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Q: 32/-20° (b) (6 - j8)(4 + j2) 20 10+j24 -

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Q: For the complex numbers w = 7 + -6 i • z = 4 - 5 i Enter the absolute value of 2w 3z in the space…

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Q: 2+7i 3-3i

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Q: 2) Suppose 1 and w are complex numbers, show that Aw =

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Q: (b) Find the conjugate, argument and modulus of the complex number Z =1+i3

A: Recall: If z= x+iy , then (i) Modulus of z , z=x2+y2(ii)Conjugate of z is z¯ =x-iy(iii) Argument =…

Q: Use DeMoivre’s theorem to find (–8)1/3. Express your answer in complex form.

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Q: Plot the complex number and its complex conjugate. -8 - 9i Imaginary axis Imaginary axis Imaginary…

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Q: Let i denote the square root of-1. For the two complex numbers z = 3e and w = 6eT find z, w. Give…

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Q: (b) Given z is the conjugate of a complex number z such that z=6+8i Find the complex number z whose…

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Q: The absolute value |z| = Va² +b² represents the distance of z from 0, and more generally, u – v|…

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Q: Solve over the set of complex numbers. x +32 0 2x2 -10 = -50 17. 18. 19. 3x2 =-12 %3D

A: We have to solve

Q: 16. Simplify √ 18a². √3a²b. Oa²√54b √6a²b √6a¹b 3a²√6b 17. Which expression represents 625p¹ - 16…

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Q: Determine the absolute value of the complex number z = 3 + 4i

A: Given: z=3+4i

Q: Find the midpoint between the pair of complex numbers. (-5 - 8i) and (-3i) O 2.5 + 2. 5i O-2.5 5. 5i…

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Q: Find the difference between the complex numbers. (4 – 7 i)- (5+ 6 i )-(-1-13 i) (4 – 7 i)- (5+…

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Q: Let z be a complex number. Then sin (3z) -i is bounded in C . TRUE OR FALSE

A: It is an application of Linville's theorem

Q: 3. Determine all complex numbers z for which |2z – 1| < 2|2 – i|.

A: The given problem is to find all the complex numbers that satisfies the given complex inequality.

Q: Find the distance between the complex numbers. z1 = 9 - 9i z2 = 10 - 9i 1.)26.2 2.)-1 3.)-26.2…

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Q: What is the complex conjugate of 2 – 3i ?

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Q: 4. Perform the following operations involving complex numbers: a. (2 + 7i) + (3 – 4i) b. (9 + 5i) -…

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Q: Find the sum of the complex numbers in the complex plane. Imaginary axis 10 8 (4, 7) 6 4 2 6 8 Real…

A: To find :               The sum of complex number in complex plane.         Adding/Subtracting…

Q: What is the algebraic form of the complex number 13 e 12+5i 5-12i 12-5i 5+12i

A: We will use the basic theory of complex numbers to answer this question.

Q: 2. Divide the complex numbers. 7+ 31 7- 3i 20 + 214 20. 21 29 29 1-i 29 – 29i O1+i

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Q: Is the complex number z=e2e1+i pure imaginary? Is it real pure? Write its imaginary part, its real…

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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: I submitted a question on write the complex # in standard form -9i^2 - 3i the answer you supplied is…

A: Simplify the given complex number as follows.

Q: a

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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: Find the difference of the complex numbers in the complex plane. (3 + 21) – (5 + 3/)

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Q: 1-A) Express the result of the following complex number expressions in both rectangular ( Re + j Im…

A: Solution

Q: - 4 as a complex number (in terms of i): |-4 =

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Q: as a complex number in Use FOIL to multiply and write the expression standard form -30) (-7+2)(-4…

A: Given that: 1. (-7+2i)(-4+4i)2. (-3-2i)(-7-i)

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: 14. Which eguation demonstrates the commutative property of addition for complex numbers? (10 – 5i)…

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Q: 20. Add the complex numbers. (2 + 3i) + (4 – 24) 8 - 6i 6 - 5i 6+i 6+ 5i 6 - i

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Q: Determine the absolute value of the complex number z = 5 + 12i

A: We have to find absolute value of complex number: z=5+12i We know that if we have complex number…

Q: Vrite cach quotient as a complex number. 28. 31 29. 3-21 21. 27. 5

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Q: Plot the complex number and its complex conjugate. -3 + 2i Imaginary axis 10 8 Imaginary axis…

A: given complex number is -3+2i plot the graph for complex number and its conjugate

Q: b, be complex numbers and N a positive natural number such N¬I i2knx N = απ Τ n = 0 to N - 1 k=0

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