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

Q: (1+i)·(10260°) (3–7i)+(9Z120°) . Express your answer in rectangular form.

A: This question is based on Complex Number.

Q: Calculate √−3+3i . How do I give my answer in a + bi form? Give the solution with smallest positive…

A: Given: z=-3+3i To Find: Write z in the form of a+ib.

Q: 2. Express the product of (3 - 2i) and (1 + 5i) divided by the product of (5 + 2i) and (-4 - i) in a…

A: Given expression is 3-2i 1+5i5+2i -4-i. Simplify the above expression as follows.

Q: Prove the law of cosines starting from A^2 = (B-C)^2

A:

Q: 1 sin4 хах 2

A:

Q: I. Solve using De Moivre's Theorem. Find the 2 square roots of 3 – 8i

A:

Q: Solve 5 sin 2 for the four smallest positive solutions

A: Topic = Trigonometry

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: Find the two smallest positive solutions (accurate to two decimal places) of 8 sin(6x) = 7: %3D Give…

A: 8sin6x=7

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: Express z = -2+4i in its trigonometric form

A:

Q: If z1 = 13 – 10i and z2 = -15 + 9i, determine the following: (2) (z1 + z2) (Rectangular Form)…

A:

Q: Find the indicated power using De Moivre's Theorem. (Express your fully simplified answer in the…

A: Given,  -32+ i-125  We have to find the indicated power using De Moivre's Theorem .

Q: (1+i)·(10Z60°) Express your answer in rectangular form. (3–7i)+(9Z120°)`

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

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: Solve 4 sin 3 for the four smallest positive solutions

A: Please go through the attached solution. I hope that this solution will help you. Thankyou . Best…

Q: 9-x2 dx. - х x2

A:

Q: sin(2z) 7. dz (z - 2n)2 Iz[=4

A:

Q: dx 2x

A: Integrate by trigonometric substitution

Q: Write full computation with using theoremas. Task is on attached image

A:

Q: Solve one of the roots of 6x^2 - 5x = 6 - 5i. Express your answer in rectangular form in 4 decimal…

A:

Q: What is the value of (3+2i)³ + (3- 2i)6

A:

Q: 9. Write in trigonometric form 4(V3 + i)

A: We will convert into trig form as following.

Q: How does the value of sine and cosine relate to writing proofs about triangles?

A: Let, ABC be a right angle triangle as shown in the figure sine(θ) = a/h cosine(θ) = b/h

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

A: To express the given expression in the form of (a+bi),where,(a,b∈R). (4+2i)(-5+4i) Solution:…

Q: Can you please help me finish solving this right triangle?

A: We use the Pythagorean theorem to find a

Q: thogonal

A:

Q: Multiply (3 cis 70°)(2 cis 110°) and express the answer in rectangular form. Give an exact answer.

A: Consider the given expression and multiply it by converting to exponential form,

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: sin(2 – 3i) cos(3 – 2i)

A: Given: sin2-3icos3-2i To find: Rectangular form of the given expression after simplifying with…

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: If a = 2i and b=-3+4i, then find the value of a²b in fully simplified form. %3D %3D

A: We plug the given values of a and b in the expression.…

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

A:

Q: Find all solutions of the equation in the interval [0, 2π)  Sqrt (3) csc (theta) + 2 = 0

A: Given : 3cscθ + 2 = 0

Q: Find the three roots of (-6 + 4i)'/3 Enter these in order of increasing angle, going from ) = ()…

A: Firstly find the tangent of angle using the below formula. If z=a+ib the acute angle θis…

Q: 4. Use DeMoivre's Theorem to find the indicated power. Write answer in rectangular form.

A:

Q: Find x and y so that the following equation is true. 4 + 8i = 6x - 24yi X = y =

A:

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: I need help solving the triangle in the picture attached.

A:

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

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

Q: /9-4х2 dx (Use Trigonometric Substitution) x2

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: Find all the solutions of the equation 2z + 3 – 4i =-1+2i i+1–4z and express them in Cartesian (x+…

A: Given equation is 2z+3-4ιι+1-4z=-1+2ι. We have to find the solution of this equation. We know that…

Q: Show use of variable substitution to factor and solve over (0,2pi) when necessary. 4. 6sin2 θ -…

A: Solve by making factor

Q: sin(2 – 3i) cos(3 –- 2i)

A:

Q: Exer. 21–46: Express the complex number in trigonometric form with 0 so<27. 25 2V3 + 2i 4 cis 37 29…

A: Given: The complex number 25) 23+2i. 29) -20i 34) -5.

Angles

In mathematics, angles constitute a very important part. Just like the concept of lines, an angle is a necessary figure that is used for measurement. How do you define its formation? It is formed when two or more lines meet at a point. The point at which two or more lines meet is known as the vertex. When the lines get inclined at this point, they do form various angles. Angles are measured from the vertex in terms of degrees.