For Exercises 55-60, find the indicated complex roots by first writing the number in polar form. Write the results in rectangular form a + bi. (See Example 9) 55. The sixth roots of 729 56. The fourth roots of 625 57. The cube roots of 27i 58. The cube roots of -125i 59. The square roots of -8 + 8V31 60. The square roots of 50 – 50V3i

Q: 5) Find the fourth root of-4-4i.

A: To find the fourth root of the below complex number

Q: 7) What are the real and imaginary parts of (1+3i)exp(-ir/4)/(6+8i)?

A: The given complex number,        1+3iexp-iπ4/6+8i

Q: For Exercises 41-42, find the indicated complex roots. Write the results in polar form using degree…

A: 41. Consider the square root of 25cos120°+isin120°. If z=rcosθ+isinθ is the given complex number in…

Q: Simplify the complex fraction. 1 4 2 64 1

A: To simplify the fraction

Q: For Exercises 9–14, find the modulus of each complex number. (See Example 2) 9. а. 20 - 21i b. -11 +…

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: 7 1一 y? 49 – 1 y?

A: We can simplify the fraction as below.

Q: 13. Use the exponential form of a complex number to write a + ib. ++) in the form

A:

Q: 1. Simplify the complex mumbers below. i (3+ 5) + (10-14) i. (3+5) - (10 -14) i. (3+ 5)(10-14i)

A: According to the given information it is required to simplify the complex numbers given in each…

Q: 22 = = Ti 2

A:

Q: 26. Use a calculator to help write the complex number in standard form. Round the numbers in your…

A: Solution: The objective is to write the given complex number in standard form

Q: Find the fifth roots for -16-16/3i

A: Consider the given complex number. z=-16-163i=x+iy x=-16  and y=-163 Convert it into polar form.…

Q: For Exercises 115–120, factor the expressions over the set of complex numbers. For assistance,…

A: " Since you have posted a multiple questions, we will solve first three questions for you. To get…

Q: 1. Detemine, whether and-5 are roots of the equation 10a –5 = 2a3 - a?.

A:

Q: ) What are the real and imaginary parts of (1+i)exp(-i/4)/W2? ) What are the real and imaginary…

A:

Q: 4. What is the simplification of the following complex expression (i? = -1) 5-i 3+i %3D a) 7/5 -…

A: Given the complex expression=5−i3+i

Q: 16. Simplify √ 18a². √3a²b. Oa²√54b √6a²b √6a¹b 3a²√6b 17. Which expression represents 625p¹ - 16…

A:

Q: What is the exponential form of the complex number 4+31? 36.87*i B 7e36,87 C 7e 53.13 D) Se $3.130/

A:

Q: 4. What is the simplification of the following complex expression (i? = -1) 4+ 3i 1- 3i 13 (9 3 A)…

A:

Q: 4 hours to 30 minutes turn that into simplest form

A: Our objective is to find simplest form.

Q: 2. Simplify the expression (3 - 4i)(1 + 5i) - (2 - i). Show your work. Answer:

A:

Q: How do I plot -7+i and 8-6i os it on the -7 and 8 since -6 is on th imaginary line

A: To plot these complex numbers, we need to draw a complex plane.Complex Plane: Here, X-axis is the…

Q: What is the conjugate of - 3 + 4i?

A: Any number of the form a+ib where a and b are real numbers and i=-1 is called a complex number. The…

Q: What is the simplified form of the complex mumber А. 1 C. 8+ 6v3i D.-10-i В.

A:

Q: (2+31) Simplify (7-4i) 16)

A: We have to simplify the following -  (2+3i)(7-4i)

Q: For Exercises 35–36, given complex numbers z1 and z2, a. Find z1z2 and write the product in polar…

A:

Q: 3. What are the roots of - 5x2 36 =0 1. (3i, -3i,-2, 2} 2. (-2i, 2i,-3, 3} 3. (9,-4} 4. {-9,9,-4i,…

A:

Q: What is the simplified complex expression of (4.33 +2.5i)??

A: Solution :  Given that (4.33 + 2.5i)2

Q: 2 - Step 1 2 The LCM of 2 - is x2 10 2 Step 2 Multiply the numerator and denominator of the complex…

A:

Q: 43 Explain in detail with at least two sentences how to represent the difference of z1 and z2…

A: Given data ÷ Z1=8 - i and Z2=-9 + 2i

Q: How do I multiply (2+3i)(4+6i) and what is the answer in its simplest form

A:

Q: 13. Use the exponential form of a complex number to write a + ib. (+)* +i in the form

A:

Q: Find the four fourth roots of -8 + 8√3 i.

A: Given  The complex number is -8 + 8√3 i .

Q: For items 8 & 9, express the complex number in rectangularform. 8. 4 cis - A. 1+ iv7 B. 2+i 2V3 C. 2…

A:

Q: What are the roots of x*-25? x= + 5, x = ± 5i %3D B x= + /5 only C. x = ± /5, x= ±i/5 %3D D…

A: using identities

Q: (a) Simplify i*+1 in real and imaginary parts.

A: As there are two questions given ,i only do the first.

Q: 2.2 Simplify the complex power (E) -2i and leave your answer in its simplest form.

A: Given that, the complex expression is 1+i1-i-2i.

Q: Write the quotient in rectangular form. 4 cis 320° 12 cis 95° ..... 4 cis 320° 12 cis 95° (Simplify…

A: topic - complex numbers

Q: What are the steps to solve for θ in the equation 2sin⁡(θ)=0.651

A: We have to find theta

Q: 2+31 ++8, Express the answer in rectangular form. B. Evaluate the expression C an

A:

Q: For #3-4, solve the quadratic equation over the complex numbers. 3. x2 - 17x = 11 4. (x + 3)2 + 3 =…

A:

Q: Simplify the given complex fraction. 50 5 + Preview 100 s2

A: Given fraction is

Q: 10. Write 2e' the complex form of a + bi.

A: Given exponential form, 2eπ3i

Q: In Exercises 1–4, write the complex number instandard form.1. 6 + √−4 2. 3 − √−253. i2 + 3i 4. −5i +…

A: We have to write the complex numbers in standard form: 1. 6+-42. 3--253. i2+3i4. -5i+i2 We know that…

Q: 9) Simplify, then write your result in standard form: (6 + /-9) – 2i + 10 – J16. (a) 16 - 3i (b) 13…

A:

Q: 7. Write down complex numbers in the trigonometric and exponential forms a) z = -21; b) z= 5; c) z=…

A:

Q: the complex number z = 18 + 18j in trigonometric form Group of answer choices   19.7(cos23.96°+ ?…

A:

Q: Remove the radical from denominator: 3 3+√3 Select one: O a. O b. O C. O d. 3-√3 2 X+ 2 After…

A: This question is related to simplification of fractions, we will solve it using given information.

Q: 110. Discuss the difference between the products (a + b)(a – b) and (a + bi)(a – bi).

A:

Q: 7. Which of the following most precisely describes the roots of the equation 3x2 + 4x -1 = 0? A 1…

A: Using quadratic formula