4.5 Finding a Power of a Complex Number In Exercises 91-96, use DeMoivre's Theorem to find the power of the complex number. Write the result in standard form. 91. [s( i sin + i sin 93. (2 + 31 95. (-1+ 94. (1 - 96. (3 - i

Q: Write the complex number in rectangular form. 5 cis 45° The complex number is (Simplify your answer,…

A: We will find the rectangular form.

Q: Express 8/-121 as a complex number (in terms of i): 8-121 = %3D

A: The expression is given as , -8-121 Express as a complex number.

Q: N=-7+1li %3D

A: Given complex number Z=-7+11i

Q: Plot the complex number. 6/6 - i Imaginary Imaginary axis axis 20 20 10 10 Real Real - 20 --- 10 10…

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Q: Plot the complex number and its complex conjugate.

A: Let the complex numberz = x + iywhere x = Real part y = imaginary partAnd its complex conjugate is…

Q: Proof Prove that the product of a complex numbera + bi and its conjugate is a real number.

A: Given complex number is a+ib. To prove that the product of given complex number and its conjugate is…

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: Divide complex numbers: 5- 21 1-21

A:

Q: How is the product of a complex number and a real number represented on the complex plane? Consider…

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

A: Demoivers theorem

Q: Plot the complex number in the complex plane. 2 + 2i -2 +++++ 2. 2. す

A: Real and imaginary part of the complex number are 2 , 2 respectively.  It is in first quadrant and…

Q: In Exercises 76–77, find all the complex roots. Write roots in polar form with 0 in degrees. 76. The…

A: 76. 49(cos 50° + i sin50°)77. 125(cos165°+i sin165°)

Q: Find the modulus and argument of the complex number (2+i/3-i)2. Also express -5+ 5i in polar form

A: 2+i3-i2=2+i3-i·3+i3+i2=6+2i+3i+i29-i22=6+5i+-19--12=5+5i102=25+50i+25i2100=25+50i+25-1100=50i100=i2=…

Q: 111. Give an example of a complex number that is its own conjugate.

A: Given, Give an example of a complex number that is its own conjugate.

Q: Plot the complex numbers –4+i and 6–Ni in the complex plane. Imaginary Axis 8- 6-+ 5- Real Axis -8…

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Q: Write the complex number in rectangular form. 9 cis 135° The complex number is (Simplify your…

A: Given complex number is 9cis 135°

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

A:

Q: In Exercises 77-80, determine whether each statement is true or false. If the statement is false,…

A: Statements are given , we have to check whether it is true or false

Q: Plot the complex numbers 2i and -5+3i in the complex plane. Imaginary Axis 7- 6- 5- ? 4 3- 2- 1-…

A: We will plot the points.

Q: Yes or No? If No, give a reason. Is every real number also a complex number?

A: Let a and b be real numbers. Then any number is called a complex number if it is of the form a+ib.…

Q: How do you find the nth root of complex numbers and provide an example?

A: To find the nth root of a complex number first convert it into a trigonometric form. z=r [cos θ +i…

Q: What is a complex number? Give an example of a complex number, and identify the real and imaginary…

A: A complex number z can be written in the form z = a + ib, where a, b are real and i = sqrt (-1).…

Q: Plot the complex number. 3 + V3i Imaginary Imaginary axis axis 4 3 + V3 i Real Real -4 -2 2 4 axis…

A:

Q: Find the sum of the complex numbers in the complex plane. Imaginary axis 10 8 (4, 7) 6 4 2 6 8 Real…

A: To find :               The sum of complex number in complex plane.         Adding/Subtracting…

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

A:

Q: Find a complex number z such that |sinz|>1

A: We have to find a complex number z such that |sin z|>1.

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

A: DeMoivre's theorem says that for any complex number of the form rcosθ+isinθ, the power of the…

Q: Write the complex number in trigonometric form. (Let 0 < 0 < 2n.) z = Imaginary axis 10아 5 z = -4 -…

A: The given complex number is  Z= -4+0i  Here the imaginary part of this complex number is 0 .

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: 1-181 Q2- The complex number z satisfies the equation 42 - 37 2-4 Then

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Q: I multiplied two complex numbers in polar form by first multiplying the moduli and then multiplying…

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Q: Explain geometrically or algebraically how magnitude of a complex number is equivalent to…

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Q: 6+5i -6-3i 2s

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Q: Express v-100 as a V-100 = complex number in standard form: a + bi Preview

A: We put a+bi=√(-100) and solve it.

Q: 12. Use Demoivre's theorem to find the power of the complex number. Write answers in rectangular…

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Q: Use DeMovier's Theorem to simplify the complex number ( 3 + 2i). Report below the complex number in…

A: Here we will use DeMovier's Theorem to simplify the complex number (3+2i)^5.

Q: Plot the complex number. 3 - V3i Imaginary Imaginary axis axis 4 2 3 - V3 2 Real Real -2 2 4 axis -4…

A: Here if you take Real axis as vertical axis and imaginary axis as horizontal axis then only option 4…

Q: Find the difference of the complex numbers in the complex plane. (3 + 21) – (5 + 3/)

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Q: 5–6 ■ Yes or No? If No, give a reason.5. Is every real number also a complex number?6. Is the sum of…

A: (5) Consider the given information as, Is every real number also a complex number?

Q: 1. What is complex number & conjugate complex number? Prove that the sum and product of two complex…

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Q: Write the standard form of the complex number. 5(cos(135°) + i sin(135°)) Plot the complex number.…

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Q: 7. Plot the complex number 3 - 6i

A:

Q: Enumerate 2-3 applications of complex numbers. Also, briefly discuss its importance

A: For most human tasks, real numbers (or even rational numbers) offer an adequate description of data.…

Q: Determine the absolute value of the complex number 2 - 3i.

A: Absolute value of complex number z=a+ib is represent by z and  given as z=a2+b2