Determine real part, imaginary part and absolute value of the following complex numbers: a) z = b) z = 2e-sin/2. c) :

Q: Express the complex number in trigonometric form with 0 ≤ θ < 2π.-2 - 7i

A: z=-2-7i Now, r=-22+-72=53 & θ=tan-1yx=tan-1-7-2=π+tan-172      ∵The given complex number lies in…

Q: Write the complex number in polar form with argument 0 between 0 and 27. -V2 + Või

A: Given,         -2+6iWe know that,          The polar form of a compex number is given by…

Q: Use DeMoivre’s Theorem to find the indicated power of the complex number [4(cos 15° + i sin 15°)]3.…

A:

Q: Use DeMoivre’s Theorem to find the indicated power of the complex number [√3 (cos 5π/18 + i sin…

A:

Q: Write the complex number z = 4-4/3i in trigonometric form (sometimes called polar form). Express the…

A:

Q: Use DeMoivre's Theorem to find the indicated power of the complex number. Write the result in…

A:

Q: Express the complex number in trigonometric form with 0 ≤ θ < 2π.-4 + 2i

A: z=-4+2i Now, r=-42+22=20=25 & θ=tan-1yx=tan-12-4=π-tan-112     ∵Given complex number lies in…

Q: Express the complex number in trigonometric form with 0 ≤ θ < 2π.√3 + i

A: 3+i

Q: Write the complex number==-4+4i in trigonometric form (sometimes called polar form). Express the…

A:

Q: Express the complex number in trigonometric form with 0 ≤ θ < 2π.-4 - 4i

A: Express the complex number in trigonometric form with 0 ≤ θ < 2π.-4 - 4i

Q: Use De Moivre’s theorem to change the given complex number to the form a + bi, where a and b are…

A: Given: Let z=-1+i8  To Find: To change the given complex number into a+ib form using De Moivre’s…

Q: Given two complex number (2 + i) and (-3 + i), find the distance between the two numbers on the…

A: NOTE: Refresh your page if you can't see any equations. . two complex numbers are

Q: Use DeMoivre's Theorem to find the indicated power of the complex number. Write the result in…

A:

Q: Find all complex numbers z satisfying z³ = 27i and give your answer as a comma-separated list of…

A: We have to find Z value

Q: Let z be a complex number. Then cot(5z-pi) = cot(5z)?

A:

Q: Write the complex number z =-2/3 -2i in trigonometric form (sometimes called polar form). Express…

A:

Q: Use DeMoivre's Theorem to find the indicated power of the complex number. Write the result in…

A: DeMoivre's theorem states that (cos θ + i sin θ)n = cos n θ + i sin n θ, where i is the square root…

Q: Convert the rectangular form of the complex number 2 – 2i into polar form. Show all work and label…

A:

Q: plot the point in the complex plane corresponding to the number (square root 3)-i. also determine…

A: From given, real number is,

Q: Write the complex number = = 4+6i in trigonometric form (sometimes called polar form). Express the…

A:

Q: Use De Moivre’s theorem to change the given complex number to the form a + bi, where a and b are…

A: 1-i10 Consider, z=1-i Now, z=12+-12=2 & θ=tan-1yx=tan-1-11=2π-tan-11     ∵The complex number 1-i…

Q: The complex number (−9+7i)/(9+5i) rewritten in Cartesian form is?

A:

Q: Write the complex number : = 5+6i in trigonometric form (sometimes called polar form). Express the…

A: A complex number is given by, z=5+6i. The objective is to write the given complex number in the…

Q: Write the complex number 8 – 5i in polar form. Give approximate values. Express the angle in…

A:

Q: Use De Moivre’s theorem to change the given complex number to the form a + bi, where a and b are…

A: The given complex number is, 1+i12. The objective is to change the given complex number to the form…

Q: Find the distance between the complex numbers in the complex plane. -з - 6і, 6 + 2i

A:

Q: Express the complex number in trigonometric form with 0 ≤ θ < 2π.-4√3 + 4i

A: Given: -4√3 + 4i Here  x=-43, y=4r=x2+y2=-432+42r=163+16=64r=8                        ... taking…

Q: Use DeMoivre's Theorem to find the indicated power of the complex number. Write the result in…

A: By DeMoivre's Theorem, [2(cos 20° + i sin 20°)]3 = [23(cos 60° + i sin 60°)]. We know that cos60∘…

Q: Use De Moivre’s theorem to change the given complex number to the form a + bi, where a and b are…

A: 3+3i5 Consider, z=3+3i Now, z=32+32=32&θ=tan-1yx=tan-133=tan-11=π4 Now trigonometric form is,…

Q: Find the product of the complex numbers z1 = cos π/6 + i sin π/6 and z2 = cos π/4 + i sin π/4. Leave…

A: the given two complex numbers are: z1=cosπ6+isinπ6z2=cosπ4+isinπ4 we have to find the product of the…

Q: Write the complex number –2 in polar form with argument 0 between 0 and 27.

A:

Q: Express the complex number in trigonometric form with 0 ≤ θ < 2π.-20i

A: -20i

Q: Express the complex number in trigonometric form with 0 ≤ θ < 2π.2 + i

A: Consider the provided information, 2+i  Express the complex number in trigonometric form with 0 ≤ θ…

Q: Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a…

A: Given complex number 3-4i    Point can be taken as (x,y)=(3,-4)      r=√(X2+y2)    r =√(32+(-4)2)…

Q: Write the complex number Z = 5 /3 +5i in trigonometric form (sometimes called polar form). Express…

A: Given,           z=53+5i     We know that,          The polar form of a complex numbe z=a+ib is…

Q: Express the complex number in trigonometric form with 0 ≤ θ < 2π.2√3 + 2i

A:

Q: Express the complex number in trigonometric form with 0 ≤ θ < 2π.2 - 2√3 i

A: Given complex number is: z=2-23i Let us consider, r cos θ=2r sin θ=-23 Then we get,…

Q: Use DeMoivre’s Theorem to find the indicated power of the complex number (1 - i√3)2. Write answers…

A: Known theorem: cosθ+isinθn=cosnθ+isinnθ.

Q: Use DeMoivre's Theorem to find the indicated power of the complex number. Write the result in…

A: According to demoivre theorm ,for any complex no r ( cos∅+i sin∅)ⁿ can be written as = rⁿ(cosn∅+ i…

Q: Use de Moivre’s formula to find the Cartesian form of the complex number  (-2 + 2√3i)7

A:

Q: Write the complex number in trigonometric form. 3j 3j =(cos+jsin) (Use angle measures greater than…

A:

Q: Express the complex number in trigonometric form with 0 ≤ θ < 2π.4 - 3i

A: Given: z=4-3i We know that any given complex numberz=a+ib can be written in polar form as below…

Q: Write the complex number z = 5-5/3i in trigonometric form (sometimes called polar for Express the…

A:

Q: Let z be a complex number. Then cot(5z-pi)=coth(5z)?

A: According to the given information, it is required to check whether the given statement is true or…

Q: Let z be a complex numbers. Then cot(5z-pi)=?

A: The objective is to find cot(5z-pi).

Q: Express the complex number in trigonometric form with 0 ≤ θ < 2π.-2 - 2i

A: Solution: Consider the given complex number is: z = -2 - 2i The trigonometric form of a complex…