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

Q: Write the complex number in polar form with argument 0 between 0 and 2n. -1 - V3i

A: Given query is to write the expression in Polar form.

Q: Does the Theorem (Roots) have to be used to find the nth roots of a complex number, or can other…

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: Suppose z is a complex number that possesses a fourth root w that is neither real nor pure…

A:

Q: Write the complex number in polar form with argument 0 between 0 and 2n. 7 - 7i

A: The expression of the polar form is given by z=rcosθ+isinθ Given complex number is (x+iy)=7-7i. The…

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

A: The general form of a complex number is given by z=a+ib, where a,b are two real numbers and i=-1.…

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

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: Write the complex number in polar form such that 0 less than or equal to deta less than 360 degrees

A:

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

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

Q: How would I find the magnitude of the complex number based on the given values for z?

A: To find the magnitude of the complex number

Q: When finding the n-th root of a complex number in polar form, why are there n-1 roots (solutions)?

A:

Q: 2+7i 3-3i

A:

Q: Write the complex number in polar form with argument between 0 and 2. -1-√√3i

A:

Q: Use the trigonometric form of a complex number to show that z-n = 1/zn , where n is a positive…

A: To prove the given identity

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

A:

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: Use DeMoivre’s theorem to find (–√3/2 +i/2)12. Express your answer in complex form.

A:

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

A: Given the complex numberz=10cis315°

Q: True or False The polar form of a nonzero complex number is unique.

A: The polar form of a nonzero complex number is unique.

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: Suppose z is a complex number that possesses a fourth root w that is neither real nor pure…

A:

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.

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: 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: Derive formula  for the product and division of two complex number?

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: Is the sum of a complex number and its complex conjugate a real number?

A: Consider the given statement as "Is the sum of a complex number and its complex conjugate a real…

Q: Present complex number z in algebraic form =* + 23D 35 1-3i

A:

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: Graph the complex number on the complex plane. -2 + 3i 4- 3- 2- -3 -2 -1 -2- -3- 4. 3, 1. 4.

A: Topic = Complex number

Q: Show that the conjugate of the sum (product, or quotient) of two complex numbers, z1 and z2 , is the…

A:

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.1 - 3i

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

Q: Show that the conjugate of the sum (product, or quotient) of two complex numbers, z1 and z2 , is the…

A: Let z1 = a+ib and z2 = c+id be two complex numbers. Then we get, Conjugate of z1 is = a-ib Conjugate…

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

A: answer is in next step

Q: The variable z is often used to denote a complex number and 7 is used to denote its conjugate. If z…

A:

Q: To divide two complex numbers in trigonometric form, ________ their moduli and_____ their arguments.

A: If z1=r1cosθ1+isinθ1=r1cisθ1 andz2=r2cosθ2+isinθ2=r2cisθ2 are two complex numbers intrigonometric…

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: Express the complex number in trigonometric form with 0 ≤ θ < 2π.-6i

A: Express the complex number in trigonometric form with 0 ≤ θ < 2π.z=-6i=0-6i

Q: Find the cube roots of the complex number. Express in standard form

A:

Q: Express the complex number in trigonometric form with 0 ≤ θ < 2π.-5 - 5√3i

A: Express the complex number in trigonometric form with 0 ≤ θ < 2π.-5 - 5√3i

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

A: Solution: Consider the given complex number is: z = 3 + i7 We have  z = a + ib⇒z = rcos θ + i sin θ…

Q: What is the first step in writing the complex number -1 + i in trigonomet-ric form?

A: Consider z=x+iy is any complex number, so polar form is, z=x+iy=rcosθ+isinθWherer=x2+y2θ=π-tan-1yx…

Q: Express the complex number in polar form.

A: Given:5+2iPolar form:Z=rcosθ+isinθ