Vrite the complex number in trigonometric form r(cos 0 + i sin 0), with 0 in the interval [0°, 360°). 8) 53 + 5i

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: Let z be a complex number. Then cos(3z)-i is unbounded in C. * False True

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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: ind all complex numbers z such that z=-3-4i, and give your answer in the form a+bi. Use the square…

A: Given: z2=-3-4ilet z = x+yi   then z2=x+yi2substituting z2=x+yi2 in z2=-3-4i…

Q: Find the quotient z1/z2 of the complex numbers.Leave answers in polar form.

A: we have to find the quotient of z1z2 where  z1=2cos5π3+isin5π3z2=cosπ2+isinπ2

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: Let z be a complex number. Then cos(3z)-i is unbounded in C. O True O False

A: Use z=x+iy, then show it is bounded.

Q: Express the complex number in exponential form z=rei*theta *-2pi(i) *2/(1+i)

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Q: Find the four fourth roots of z = 16(cos 60 degree + i sin 60 degree ).

A: Given  z=16cos60°+isin60° To find the fourth root De Moivre's theorem for finding complex root is…

Q: How may the following complex numbers be obtained fromz = x + iy geometrically? Sketch. 1 / z

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Q: Given that the complex numbers zı and z2 are such that z, = cos 10° + i sin 10° and z2 cos 15° + i…

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Q: 1. Use De Moivre's Theorem to write the following complex number -6 Z = (-1+i)30 in Polar Form z =…

A: The complex number z=-6(-1+i)30

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: 3. How may the following complex numbers be obtained from z = x + iy geometrically? Sketch. а. 2 b.…

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Q: Let z be a complex number. Then cos(3z)-i is unbounded in C.* True False

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Q: Let z be a complex number. Then cos(3z)-i is unbounded in C. * False O True

A: From Liovilles thm we can say Every non constant entire function is unbounded.

Q: When a complex number z is written in the polar formz = r(cos θ + i sin θ), the nonnegative number r…

A: Given- When a complex number z is written in the polar form z=rcosθ+isinθ, the nonnegative number r…

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: Find the quotient z1/z2 of the complex numbers.Leave answers in polar form.Express the argument as…

A: Given : two complex numbers as  z1=20cos75°+isin75°z2=4cos25°+isin25° To find : The quotient z1z2.…

Q: The complex number Z1and Zzare given by, Z1 = 3 – 5i and Z, = -1+4i Determine: 221 + 5Z2 O1+ 10i 01-…

A: Given: Z1=3-5i & Z2=-1+4i We know that; a+bi±c+di=a±c+b±di And ca+bi=ca+cbi, where c is scalar.

Q: Sixth roots of 64i (a) Use the formula z = 0+27tk cos +i sin 0+27tk to find the indicated roots of…

A: We have to find the sixth roots of 64i, using the expression zk=rn(cosθ+2πkn+ i sinθ+2πkn) First we…

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 cos(7z)+3i is unbounded in C. * True False

A: From the question image that you have uploaded, only 1 complete question is visible, which is the…

Q: Express the complex number z = 8 in polar form r(cos 0 + i sin 0). Select the correct answer below:…

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Q: Express the complex number z = 4 – 4/3i in polar form r(cos 0 + i sin 0). Select the correct answer…

A: Given: z=4-43i

Q: How may the following complex numbers be obtained from z = x + iy geometrically? Sketch. a. (-z) b.…

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Q: 11 Convert the complex number 8( cos 11T + i sin to polar form. Give exact answers for r and 0 (no…

A: Given :- Polar form, 8(cos(11π/6) + i sin(11π/6))   where, θ = 11π/6 and r = 8   = 8(cos(11π/6) + i…

Q: 16. SHOW ALL WORK Given the two complex numbers in trigonometric form, perform the indicated…

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Q: The roots of the complex number z = (2)¹/2 is Wo = √2 [cos+ i sin], w₁ = √2 [cos+ i sin true false

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

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Q: Find the quotient z1/z2 of the complex numbers.Leave answers in polar form.Express the argument as…

A: r(cos x + i sin x)= r eix

Q: What is the rectangular form of the complex number z = 40 e %3D O z = -20 + 34.64 j O z = 40 (cos120…

A: We know that Euler's formula  e^(jx) = cos (x) + j sin(x) Here given complex number is  z = 40e^(j…

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: z is a complex number with |2| = 6. The triangle formed by z, z?, z° has a right %3D angle at z.…

A: Use the following formulae, to obtain the solution. i2=-1 x+iy=x2+y2 If z=x+iy is a complex number,…

Q: Find the quotient z1/z2 of the complex numbers.Leave answers in polar form. z1 = 10(cos 10° + i sin…

A: We have given complex numbers z1 = 10(cos 10∘ + i sin 10∘)z2= 5(cos 5∘ + i sin 5∘) We have to find…

Q: Determine u = cis(pi/16) v = cis(5pi/16) are two of the nth roots of some complex number z.what is…

A: Given: Determine u = cis(pi/16) v = cis(5pi/16) are two of the nth roots of some complex number…

Q: Simplify the complex number z = j(-1+ j) and plot the result on your Argand diagram. Then, find the…

A: Given :           z = j(-1 + j)        To simplify z and to plot the result on Argand diagram.…

Q: What is the result of multiplication of complex numbers -V3 + i and (cos + i sin ) ? A)1(cos 뚫 +isin…

A: We have to multiply the given complex numbers . The solution is following

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: Express the complex number z = -V2 - V2i in polar form r(cos 0+i sin 0). Select the correct answer…

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Q: p and q are complex numbers such that p| = x + 2, |q| -žx – 1, and |p+q] = 2x + 4 %3D On what…

A: I have provided solution in step2

Q: Let z be a complex number. Then cos(3z)-i is unbounded in C. * True False

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Q: =(-1= v3i)³

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Q: Ifz is a complex number, then sin-z can be written as (A)-i In iz+ (1-z) (B)t In [iz + (1 -z)]…

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Q: a) Express the complex number Z 10 (cos 150° +i sin 150° ) in rectangular and exponential form. V3…

A: (a)z=10(cos 150°+i sin 150)where r=10and θ=150*π180=56πExponential form is z=reiθz=10ei5π/6In…

Q: Find the quotient z1/z2 of the complex numbers.Leave answers in polar form.Express the argument as…

A: the given complex number are: z1=cos 70°+i sin 70°z2=cos 230°+i sin 230° we have to find the…

Q: Write the complex number in trigonometric form r(cosθ+isinθ) with θ in the interval [0°,360°). 2+2i

A: Given complex number 2+2i. The objective is to write the complex number in the form  r(cosθ+isinθ).

Q: 2(2) A complex number z = v2(cos+i sin ), find In ( Z.Z' )

A: z = √2(cosπ/4 + i sinπ/4)  z = √2(1/√2 +i/√2 )  z = (1+i)  z* = 1-i

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.