Use De Moivre’s theorem to find the sixth roots of the complex number Z = -2 – 2i . Show all the roots in rectangular form and graph them on one Argand Diagram.

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

A: We have to find The real and imaginary part of the complex number. z=-23i

Q: Graph the complex number, find its modulus and put the complex number n in polar form with arguement…

A: Given complex number z = -5 + 5√3i.Graph the complex number.

Q: Find all the complex numbers x that satisfy the equation x5 - ix4 + 5x3-5ix2 + 6x - 6i = 0. Then…

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Q: Represent the complex number geometrically.2i(2 + 3i)

A: given 2i(2+3i) =4i-6=-6+4i It is represented in a complex plane. where x-axis represents real value…

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: 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: Express the complex number in trigonometric form with 0 ≤ θ < 2π.-10 + 10i

A: We have given  z = -10 + 10i    Now, z can written as reiθ    r =  (-10)2+ 102              [ As if…

Q: Represent the complex number geometrically.(-3i)(2 - i)

A: -3i2-i=-3i2-3i-i=-6i+3i2=-6i+3-1=-3-6i

Q: Find the square roots of the given complex number by using result (10) and then confirm the result…

A: Given:  1) 2-3i2) -2-i Find the square roots of the given complex number by using result (10) and…

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

A: z = a + ib                          where,  a…

Q: Find the product (3 - 4i ) (5 + 6i ), and express the result in the standard form of a complex…

A: Consider the given expression as 3-4i5+6i

Q: This complex number is pure real? 1-2i/i and why?

A: For a complex number, z=x+iy, where x is the real part, y is the imaginary part. The complex number:…

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

A: Given, To Evaluate, the complex number in trigonometric form with 0 ≤ θ < 2π.1 - i Here  a=1 and…

Q: (5-8) and (-31)

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Q: Find all fourth roots of 1 in the complex numbers.

A: Let x be the fourth root of unity x=14 x4=1 x4-1=0 Equation 1

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

A: Consider the complex number  −12i

Q: The complex cube roots of 1,Find all the complex roots. Write roots in rectangular form. If…

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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: 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: (7-21) and (5 + 8i)

A: Find the distance between and the midpoint of each pair of complex number (7-2i) and (5+8i) .

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

A: 4-1+2i

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

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

A: (1+5i)

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: Plot the complex number z = 3 and find its absolute value.

A: Consider the given: z=3It can be written as:z=3+0iComparing z=x+iy,here,x=3,y=0

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

A: Given complex number: i3

Q: Find the quotient (2 - 3i)/(3 + 4i) , and express the result in the standard form of a complex…

A: We have given quotient 2-3i3+4i Then,…

Q: Find the real and imaginary parts of the complex number. 5 - 7i

A: Known fact:  For a complex number z=x+iy, x is called real part and y is called imaginary part.

Q: Find all the complex roots of (4 – 4i)1.

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Q: Plot the complex number z = 2 + 5i and find its absolute value.

A: Given:z=2+5i

Q: Find the principal root of the complex number: (1– (2+ 4i)²

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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: Plot the complex number z = 4i and find its absolute value.

A: To plot the complex number z=4i and find its absolute value.

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

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Q: Express the complex number in trigonometric form with 0 ≤ θ < 2π.4 + 5i

A: Given that, the complex number 4+i 5 Express the complex number in trigonometric form with 0 ≤ θ…

Q: Plot the complex number z = 4 - i and find its absolute value.

A: In the Argand plane, the real axis is the x-axis and the imaginary axis is the y-axis. The absolute…

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: Plot the complex number z = 3i and find its absolute value.

A: Plot the complex number z = 3i and find its absolute value.

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: Find the difference of the complex numbers in the complex plane. (4 + 2i) - (5 + 4i)

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

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Q: Use De Moivre's Theorem to find the complex number raised to a power. Leave your answer in CIS form.…

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Q: Find the complex conjugate of (2+3i)/(1-i)

A: We find complex conjugate of (2+3i)/(1-i)

Q: Find the square roots of the given complex number by using result (10) and then confirm the result…

A: We can find the square root of complex number by using the formula.

Q: Find the roots of complex numbers. z5 = 4i

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

A: Concept  -If a complex number is given as - z = a+biThen,a = real partb = imaginary part

Q: Find and graph all the roots in the complex plane. (3 + i4)

A: this is a problem of complex analysis.

Q: Find all cube roots of the complex number −1 + i

A: We have to find all the cube roots of the given complex number.