ri(cos 01 + i sin 01) r2(cos 02 + i sin 02) [cos(. -) + i sin The quotient of two complex numbers in polar form is found by. and their moduli their arguments.

Q: Find a complex number z such that |sin(z)| > 1.

A: The objective is to find a complex number z such that |sin z|>1.

Q: 1. Prove Euler's formula: Let z e C (the set of all Complex numbers). Then: eiz = cos z +i sin z

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Q: Ihe complex number z is defined by z = a + ib, where a and b are real. The complex is denoted by z*.…

A: Given: z=a+ib, z*=a-ib

Q: 1296. Express your answer in polar form Find the four fourth complex roots ofz = and then convert…

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Q: 4 - 2i 2+5i consider the complex number z = 1+i 1-i Find |2| and arg(2).

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Q: Find the quotient of the complex numbers. Leave your answer in polar form. Express the argument as…

A: Write Z1 and Z2 in form of e^i*theta

Q: Express the complex number z = -6i in polar form r(cos 0 + i sin 0). Select the correct answer…

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Q: Write the complex number z = (-1 - (3)1/3i)16 in polar form: z = r(cosθ + isinθ). The angle should…

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Q: Find all the complex roots. Leave your answers in polar form with the argument in degrees. The…

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Q: Find the product of the complex numbers. Leave the answer in polar form. 5% 5n z1 = cos +i sin and…

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Q: Z1 Find the quotient of the complex numbers. Leave your answer in polar form. Express the argument…

A: First rationalisation the given function and then apply trigonometric identities.

Q: ri(cos 01 + i sin 01)· r2(cos 02 + i sin 02) = [cos( ) + i sin ( )] The product of two complex…

A: We know that, the product of two complex number in the polar form is found by multiplying their…

Q: For a positive integer n, the complex number z = r(cos 0 + i sin 0) has exactly n distinct nth roots…

A: for the complex number,  the nth root is given by

Q: Let z be a complex number. Then cot(5z – 1) is equal to a. cot(5z) b. coth(5z) c. -tanh(5z) d.…

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Q: Solve the complex number. 1.) arcsin (2-3i)

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Q: Find the product of the complex numbers. Leave your answer in polar form. z, = 10( cos 30° + i sin…

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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: 7T (cos+ i sin 7) in the form a + bi. 3. Write the complex number 4 (cos-

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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: (iii) Use De Moivre's Theorem to show that cos 40 = 8 cos 0-8 cos0 + 1. (iv) Hence, find all the…

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Q: Find the product of the complex numbers.Leave answers in polar form. z1 = 3(cos 40° + i sin 40°) z2…

A: The given complex numbers are z1 = 3(cos 40° + i sin 40°)  and  z2 = 5(cos 70° + i sin 70°). Compute…

Q: e the standard form of the complex number.   7 5  cos   2π 3   + i sin   2π 3

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Q: Зл 3 (cos()+ isin (4)) and z2 = 4 (cos() + isin (4)) be two complex numbers Let z1 %3D in…

A: Let z1 and z2 be two complex numbers in trigonometric (or polar) form. We have to find z1z2 , z1/z2…

Q: 21 of the complex numbers. Leave your answer in polar form. Z2 Find the quotient z1 = 35( cos 120° +…

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Q: Find the product of the complex numbers.Leave answers in polar form.

A: we have to find the complex numbers. z1=3cos5π8+isin5π8z2=10cos5π16+isinπ16

Q: 6. a. The polar form of complex number is Z = r(cos 0 +i sin0 = ret®. Proof this identity and…

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Q: Let z be a complex number. Then the solution(s) of sinhz+coshz=1/e is (are) * z=nti-1 where n is an…

A: This is a problem of complex analysis.

Q: De moivre's theorem to find the indicated roots of the complex number. use Cube roots of 343 0s 2 +…

A: The cubic roots of the complex numbers using DeMoivre's theorem for a complex number rcost+isint are…

Q: Find all complex numbers z so that z6 = 218 Express your solutions in the form a + bi, evaluating…

A: Given: z6=218 We have z6=236z=23 Let z=rcosθ+isinθ. Then, z to the power 6 gives…

Q: Find a complex number z such that |sinz|>1

A: We have to find a complex number z such that |sin z|>1.

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

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Q: 6) Divide the complex numbers, and leave the result in polar form. 8(cos 100° + j sin 100°) 4(cos…

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Q: 3(cos i sin ) and Given the complex number z1 22 = 3( cos +i sin ), express the result of 21 22 in…

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Q: Express the complex number z = - 1 - (square root 3)i in polar form: Z = r ( cos ( θ ) + i sin ( θ )…

A: Explained below

Q: Find all complex numbers z such that z=-15-8i, and give your answer in the form a+bi. Use the square…

A: Follow next step

Q: If Z1, Z2 are complex number then |Z1 Z2|2|Z1 ||Z2| True False

A: Given ;Z1Z2≥Z1Z2

Q: Find the product of the complex numbers. Leave answers in polar form." z1 = 3(cos40° + isin40°) z2…

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Q: What is the result of multiplication of complex numbers -√3+i and (cos+ i sin )? A B (cos+ i sin )…

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Q: Write the standard form of the complex number.   7 6  cos   5π 6   + i sin   5π 6

A: Step 1Given :   76 Cos 5π6 + i Sin5π6Write in standard form.

Q: Find the quotient of the complex numbers. Leave your answer in polar form. Z2 - z1 = 30( cos 100° +…

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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: = 2√√5 +11i in polar form and also represent it graphically 2Q. Express the complex number z = Hence…

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Q: Find the quotient of the complex numbers. Leave your answer in polar form. Z2 21 = 6( cos 50° + i…

A: First I have written the definition of Euler's  exponential function, just use them and easily find…

Q: 3. Show that tan z does not assume the value ±i. Does this contradict Picard’s theorem?

A: Use the definition of Picard theorems.

Q: 74. Two complex numbers a + ib and c + id are equal if and only if a = c and b = d. Use this fact to…

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Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.