When a complex number z is written in the polar formz = r(cos θ + i sin θ), the nonnegative number r isthe____ or_____ of z, and the angle θ,0 ≤ θ < 2π, is the______ of z.

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: The complex number u = a + bi is an ________ ________ of the complex number z when z = un = (a +…

A: Consider "The complex number u = a + bi is an ________ ________ of the complex number z when z = un=…

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

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Q: diven the complex number 음 cos 등 + isin. isin. A. Write the exact standard form of the complex…

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Q: Express the complex number z = -6i in polar form r(cos 0 + i sin 0). Select the correct answer…

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

A: We have to check

Q: Among the complex numbers below, which is not a result of one of the following calculations: -1+ 2i…

A: We have to check

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

A:

Q: 11.Write the complex number 3e in polar and rectangular form

A: Given:     Z = 3ei(4π/3)

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 – 1) is equal to a. cot(5z) b. coth(5z) c. -tanh(5z) d.…

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Q: The argument in converting complex numbers in polar form is computed as __. a. Cosine of the ratio…

A: If z=a+ib,  and if argument of z be θ,

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: Evaluate the given complex number. z=[tan(1-i)]^[cot(1+i)]

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

A: -1 - sqrt(3)/3 i = -1 - 0.577i (approx) This is similar as (-1,-0.577). Plotted it on graph.

Q: 15. Express the given complex number in standard polar form. 5 п -2cis 4 O a. √√2+√2i O b. √2+8i OC.…

A: Given;  -2 cis(5 pi/4) Repost the next question.

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

A: Our objective is to write the given complex number in standard form.

Q: Make this compley number in polar Form: Z - 5 +V4 i 5-6i

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Q: The complex number graphed below can be expressed in rectangular form as. -or in polar form as. Im…

A: Consider the given graph.

Q: 20) Write the complex number in rectangular form. 5(cos 195° + j sin 195 °)

A: The given complex number is 5(cos195°+j sin195°). The objective is to find the rectangular form of…

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

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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: Find all complex numbers z satisfying 4 = -8-8 3i and give your answer as a comma-separated list of…

A: Solve the following

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

A: The given trigonometry function is Use DeMoivre's Theorem to find the indicated power of complex…

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

A: The objective used to use Demoivre's theorem to find the indicated power of the complex number and…

Q: 6) Divide the complex numbers, and leave the result in polar form. 8(cos 100° + j sin 100°) 4(cos…

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Q: Evaluate and convert the complex numbers into polar form. a) a + -/5 - 2i 3 1 + 2

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Q: 1. Plot the complex number on the complex plane and write it in polar form and in exponential form.…

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Q: a) 2+2v3i b) -5+ V3i c) =V6– v2i VZi d) –3i

A: Thanks for the question :)And your upvote will be really appreciable ;)

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

A: Graph the given complex numbers as shown below.

Q: Find the distance between the complex numbers in the complex p 1 + 7i - 1 + 5i

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Q: Z1 and Z2 are two given complex numbers

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Q: Let z be a complex number. Then coth(2+ Ti) is equal to -cothz tanhz O -tanhz O None of these

A: I have solved bothe examples for first question first option is correct And for second question last…

Q: Let the left complex number be z1 and the right complex number be z2. +i sin- 43 - 4i 8 cos a) Write…

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Q: The complex number a is given by a =-2 + 5i. i) Write down the complex conjugate a*. a +a* ii) Find…

A: α =-2+5i complex conjugate =-2-5i

Q: Let z1 , Z2 and z3 be the complex numbers given in the following argand diagram. Find the complex…

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Q: Find the indicated powers of the given complex number. Express the result in polar form, then…

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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: Write the given complex number in polar form and in then in the form a + ib. You may use the De…

A: By Euler's formula we have eix=cos x+i sin x. Using eixn=einx we get the De Moivre's formula cos x+i…

Q: Question 6 Applying De Moivre's theorem intyriting the complex number(-1-im the form a+ bi, the…

A: De Moivre's theorem states thatcosθ+isinθn=cosnθ+isinnθ

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

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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).