solve the complex number using De Moivre's Theorem 483 ( - V3 2

Q: Find all complex numbers z satisfying 4 = -81

A: Find all the complex numbers z satisfying z4= -81

Q: Consider the complex number 2 + i. Working in exponential form, investigate the effect of…

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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: Represent the complex number geometrically.(1 + 2i)2

A: Represent the complex number geometrically.(1 + 2i)2

Q: Need help

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Q: Express the complex number in exact simplified rectangular form.

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Q: Find all the roots in the complex plane using De Moivre's Formula in polar form and rectangular…

A: To find the fourth roots of -1 the De Moivre's formula convert the rectangular co-ordinate to polar…

Q: Use DeMoivre's Theorem to raise the complex number to the given power. Express your solution in…

A: Compare the given complex number with the standard form and find x and y.Find theta using x and y.

Q: 9. Find the complex sixth roots of -1 -i. Leave your answer in polar form.

A: The complex number is -1-i.

Q: Factor over complex numbers into a product of linear factors x2n + x" + 1

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Q: Determine the four fourth roots of the complex number Z 3-4j, using De Moivre's theorem and express…

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Q: Prove:The addition of complex number is associative.

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Q: Find all the roots of the complex numbers using different theorems. 1 1. (-5 +j12)5

A: Let's find.

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

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Q: Change the Complex Number Z = 4|120'in to Rectangular formal. %3D

A: according to our guideline we are supposed to answer only the first question if you want any…

Q: Consider the complex number z = 10250°. What is the smallest positive integer n such that z" is a…

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Q: Suppose the product z1z2 of two complex numbers is a nonzero real constant. Sho 2 kz1, where k is a…

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Q: Express the complex number in trigonometric form with 0 ≤ θ < 2π.-12i

A: Consider the complex number  −12i

Q: Express the complex number z = 10 cis 315° in rectangular form a + bi.

A: Given the complex numberz=10cis315°

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

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Q: 67 V3 1 Use De Moivre's Theorem to express the complex number on the form a+ bi. ---1

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

A: Given :            -22 + 22i15   To change the given complex number to the form a + bi using De…

Q: 3. If z, and zz are two complex numbers, prove that

A: Let's find.

Q: If z is a complex number, show that the product of z and its conjugate is a realnumber.

A: Let z=a+ib be any complex number where a and b are real number. Then conjugate of z is z¯=a-ib

Q: Represent the complex number geometrically.4(-1 + 2i)

A: 4-1+2i

Q: 5. Determine the roots of the complex numbers studied in class. z3 = 2 – 3i %3|

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Q: Transform the complex number into its rectangular (1+5i)

A: (1+5i)

Q: Express the complex number in exponential form. z=4-6i

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

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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=1-3i3 To Find: To change the given complex number into a+ib form using De Moivre’s…

Q: Convert the complex number z = -√2 (lis (317) in its rectangular shape

A: Given: z=2cis3π4 To find: Rectangular form of given complex number.

Q: Find the real and imaginary parts of the complex number.

A: Given complex number: i3

Q: What is the complex conjugate of a complex number a  bi?

A: The given complex number is a+bi. Here a and  b  are real numbers. The real part is a and the…

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

A: -20i

Q: Solve for the six sixth roots of z-1 and show their geometric representation on a single complex…

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Q: Use de Moivre's formula to find the Cartesian form of the complex number (-1+iv3) *".

A: The given complex number is                                      -1+i3-7 De Moivre's formula:…

Q: Express the complex number in trigonometric form with 0 ≤ θ < 2π.1 - 3i

A: Consider the complex number: 1-3i. Write in the trigonometric form   A complex number a+ib in the…

Q: The modulus of a complex number x+jy is equal to

A: The modulus of a complex number x+jy is equal to

Q: Express the complex number z = 10 cis 270° in rectangular form a + bi.

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Q: Find all the roots in the complex plane using De Moivre's Formula in polar form and rectangular…

A: To convert the complex number -j into polar form a+ib=rcosθ+jsinθ, substitute 0 for a, -1 for b in…

Q: What are all the cube roots of -1 in the complex plane?

A: answer is in next step

Q: Find all complex square roots of -2+2/3i. In other words, find all complex solutions of x=- 00..

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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: Find all complex numbers z satisfying = -i

A: i = -1(i)2 = -1

Q: Show that if z1 and z2 are complex numbers then (z1/22) = Zī/22.

A: Given, z1 and z2 are two complex numbers and we have to show,

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

A: Express the complex number in trigonometric form with 0 ≤ θ < 2π.3 - 3√3i = 3 (1 - √3i) Multiply…

Q: Prove that x^2 = 4 will result into ± 2 using complex numbers.

A: Given that, x2=4

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…