b) Find : 1+i)5 (1-i)7 c) Calculate: i9 + i13 + 5i32 – 16i78

Q: Visualize the addition of ( 3+ 8i) + (4 – 4i) by plotting the initial point, and the result. 10+ 6-…

A: Given  (-3+8i)+(4-4i) = (1+4i)

Q: What is the value of  i) i3i3  and ii)  i6i6

A: Given that  i3i3 I^6i^6 To find the values

Q: Perform the indicated operation. Show all work possible. (-4+5i) -(6-9i)

A: a+ib +c+id = (a+c) +i(b+d) a+ib-(c+id) =(a-c) +(b-d)i

Q: Calculate (3 + i)*. Give your answer in a + bi form

A: Consider the complex number, Let,     z=3+i The polar form of the complex number z = a + ib is,…

Q: 4. (a) (i) Calculate (4 + 6i)².

A:

Q: Determine the equivalent when (8+8i) is raised to 1-i. Express your answer in a rectangular form in…

A: We have to find 8+8i1-i=?   The magnitude of 8+8i is = r=82+82=128=82 The argument of 8+8i is =…

Q: 18. Simplify: i9 + j21 + j2050 in form a + bi.

A: Complex number a+ib form

Q: Use De Moivre's Theorem to evaluate [-6+ 2i]6

A: Any complex number z=x+iy can be represented as  z=r(cos θ+isin θ) , where r=x2+y2, θ=tan-1 yx.  De…

Q: In this figure, m21=(15x-5) and m/2 = (10x+ 35)°. %3D %3D

A:

Q: Derive the formula V sphere 3

A: We have to derive the formula                                                VSphere=43πr3

Q: 4 -- ICI iC =(-1 4

A:

Q: tain the principle root of JZ rectangular form 3-j4

A:

Q: Write z = 2 cis 60 degree in standard form.

A: We have to write in standard form: z=2cis 60° We know that cis θ=cosθ+isinθ so for cis…

Q: If z1 = 13 – 10i and z2 = -15 + 9i, determine the following: 4z1 – 5z2 (Rectangular Form) COMPLETE…

A: For the complex number, z=x+yi, the real part is x and the imaginary part is y. If two complex…

Q: Find the value of i20 + + 2i².

A:

Q: Find the dot product of a & b when a = 8i + 3j and b = -4i - 6j

A:

Q: Simplify the expression to a + bi form: (5 + 2i)(8 + 8i)

A: (5+2i)(8+8i) = 24 + 56i  The detailed solution is as follows below

Q: r=9sin(2theta) How do I convert this into rectangular form?

A:

Q: Use DeMoivre's Theorem to find the following. Write your answer in standard form. -8 – 8i3 8+8i -16…

A: Explanation of the answer is as follows

Q: | 2+4i -3 il %3D

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: If z1 = 13 – 10i and z2 = -15 + 9i, determine the following: 4z1 – 5z2 (Rectangular Form) COMPLETE…

A: If z1 = 13 – 10i and z2 = -15 + 9i, determine the following: 4z1 – 5z2 (Rectangular Form)

Q: The dimenions of a oil tin are 26cm x 26cm x 45cm. find the area of tin sheet required to make 20…

A: Given that: Dimensions of a tin can is 26 cm x 26 cm x 45 cm.

Q: What formula is most important to use throughout algebra?

A: a2 – b2 = (a – b)(a + b) (a + b)2 = a2 + 2ab + b2 a2 + b2 = (a + b)2 – 2ab (a – b)2 = a2 – 2ab + b2…

Q: Calculate (2 – i)°. Give your answer in a + bi form

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: Calculate (1 + 2i)'. Give your answer in a + bi form

A: To calculate 1+2i7. To give the answer in a+bi form.

Q: For the given number: Z = 4 – 2i find conjugate

A:

Q: Find the quotient. Write the answer in standard form. 5+4i 3+6l

A:

Q: In AABC, m2C = 73', AB = 20 km, and AC = 29 km. Find mZB. %3D %3D

A: It is given that in ∆ABC, m∠C=73°,AB=20 km, AC= 29 km. Sketch the triangle with above information as…

Q: Express in the form , where a and b are a+bi real numbers.

A: We have to express the express in a+bi form for the given expression: 3+8i2 We know that…

Q: Express the result in trigonometry and rectangular form (1 + 2i)4 44. (1 – 2i)?

A:

Q: Multiply (6 cis 300°)(2 cis 30°) and express the answer in rectangular form. Give an exact answer.

A: According to the given information it is required to solve the expression and express the answer in…

Q: C = In(sec[=10 – 16i])

A:

Q: Find w a + bi = Jz, where a and b are real numbers. %3D -15+8i W%3=

A: Given: -15+8i And, w=a+bi=z

Q: Use De Moivnes the orem to prore (-1+i) = -2(1+) %3D

A: Given  -1+i7

Q: Use De Moivre's theorem to evaluate (-3v3 – 3i). Express the answer in rectangular form.

A:

Q: C.from trapezoid xule, evghuate (1.2

A:

Q: Find the quotient zi lza in standard form. 2= 3-3i, 22=1-i

A:

Q: 5łn(cosh(3+j6))

A: Here 'j' represent imaginary number. Some power to imaginary number are as follows:…

Q: Find the distance d between 21 1 = (-7- 6i) and %3D z2 = (-15 – 12i). %3D

A: z1=-7-6iz2=-15-12i We can say that the co-ordinates of two points are (-7,-6) & (-15,-12).…

Q: write your answer in a + bi form. (3 + 4i)20

A:

Q: Calculate ( 3 + 2i)³. Give your answer in a + bi form Question Help: Video 1 Video 2

A:

Q: Find the quotient where zi and z2 are given below. 21 = 24 cis 178° z2 = 4 cis 58° Write the answer…

A:

Q: - 2+2i 8-8i/3 4

A: Given, -2+2i8-8i34

Q: Find the distance d between z1 = (-7– 6i) and 22 = (-15 – 12i). %3D

A:

Q: Express in the form , where a and b are a+bi real numbers.

A: Let the given expression be z - z = 7+5i--8+3iz = 7+5i+8-3iz = 7+8+5i-3iz = 15+2i

Q: Consider the following definitions of imaginary numbers: x=4−2i y=6+7i z=5i Then, x+y−2z=?

A: We plug the given values in the expression x+y-2z

Q: Reconstruct the figure by removing each green shaded cube. Use the paperclip button below to

A:

Q: 3i16 - 103 1+i 2i84 + i79

A: given the expression 3i16-i1032i84+i79 we know that i2=-1…