Let rcis(8) be a complex number in its polar form, where r> 0 y 0 €], ]. Consider the following statements: I. The main argument of the number 0 – b + 27. -3+iv3 corresponds to II. Performing the operation 2(-3+iv3) 60² + 57 2r° /3cis 6 as results. Of the above statements, which one (s) are certainly true? a. None b.I c. I and II d.II

Q: Find the principal arguments (in radians) of all 4th roots of a complex number having principal…

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Q: Express each of the folowing complex numbers in the form x + yi: (3 - 4)5 (4 + 37)

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Q: 10 Express the given complex number in rectangular form 1+/3 Answer: a. b. --V d.

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Q: Let Find formulas for the entries of M", where n is a positive integer. (Your formulas should not…

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Q: a.) (3 - 4i)(2 + 5i) 10/60 + 20/-45

A: Solution:

Q: (-√3-i)5 (2+2i)³(-1+√3) 1. Find the 5th roots of - and plot them in the complex planc.

A: Given complex number: z=-3-i52+2i3-1+3i8 To find: 5th root of complex number. Plot the points on…

Q: Let -6 M-[d] = Find formulas for the entries of M", where n is a positive integer (Your formulas…

A: The given problem is to find the matrix Mn for the given matrix M. Given matrix, M = [-6 -5 ; 5 -6].

Q: 2) Consider complex numbers z₁ = 4-3i and z₂ = −6+4i and compute a. Z₁ Z₂ b. 21 Zz C. Z1

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Q: Express 3-i/2+3i  in the form a + bi

A: Rationalise i^2=-1

Q: 3. Evaluate the following complex number a. (30460° +20<-20°) b. 302-30° +(4-j3)(3+j4)(4-j5)* C.…

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Q: (а) —3 i, (b) (3 – 5i) – (1+ 5i) + i, -3 (c) i i, %3D + ||

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Q: IN! Write each complex number in standard form. 4 10. 25 Choices for 10-16: 1 A) 11. B) C) -- 49 D)…

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Q: the argument of the Complex number: Z= ¹+√ √B-j

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Q: Find the principal argument and exponential form of z = .

A: (e) The given complex number is z=i1+i. Rewrite the above complex number in the usual form z=x+iy as…

Q: Let z1 and z2 be complex numbers. Which of the following statements are always true? (i) Re(z1z2)…

A: Complex analysis, modulus of the complex number

Q: Q1/ Answer two only from the following: 1. Find the Multiplication Product of: -3m (Z, = 1+ v3 i) By…

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Q: (b) Let A1, A2,, A46 be the roots of (5 – 2i)/46. Show that 46 II ^.A; = = 29 i=1

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Q: Find the modulus and argument of the following complex number. z= (3+2j) (- 1+2j), giving the…

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Q: 11. Write the quotient of the complex numbers in the standard form z=x+ iy. 3+i 1-2i

A: If you like the solution then please give it a thumbs up.... The Answer is:           Standard form…

Q: (a) (b) (c) (d) (1+2i) ² 2 1/(1+i) √3-4i ein/4

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Q: 2z - 8| 0 | ² + |z + i|² < 2. ≥ 1, show that 1+z+z²+

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Q: 4. What is the simplification of the following comple expression (i = -1) 4+3i 1– 3i 13 9. 1 3 A) 10…

A: 4+3i1-3imultiply and divide by…

Q: 4. What is the simplification of the following complex expression (i? = -1) 5-i 3+i

A: To simplify the given complex expression:- 5-i3-i

Q: 2+J3 7-18 a) + 1-16 -5+/11 b) (5210°) (102-40°) (42-80°) (-6250°)

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Q: bers are conjugate. If z, and z2 are two non-zero complex numbers st jal arg (2) ) - arg (z2 ).

A: Since we know that, | Z1 + Z2 | = |Z1| + |Z2| only when the the point Z1 , Z2 and origin are…

Q: 7. Express the complex number 1/(1+ jV3) in the form Aejº

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Q: EX' 1) show That. the ring of Complex numbers can be imbed iny in ariny 2x 2 matreces.(M 241

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Q: #2. If 2₁ and 2₂ are two complex numbers, show that 12₁-221² + 12₁ +221² = 2 ( 1211² + 122 1²).

A: 2. Let z1 = a + bi and z2 = c + di be two complex numbers.      Then,          |z1|2 = a2 + b2…

Q: Write the following complex expression in Cartesian from. Simplify as much as possible. 10 (√6 +…

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Q: a

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