Given that i is the base of the imaginary numbers, justify why i' must be equal to -i?

Q: |a|, called the of a, represents the distance from on the number line. to

A: It is known that a represents the absolute value if a.

Q: Facor : (i is the imaginary unit ) Into: K+1

A:

Q: If x and y are positive numbers with x > y, show that a triangle with sides of lengths 2xy, x 2 -…

A: To Determine: show that a triangle with sides of lengths 2xy ,x2-y2 ,x2+y2 is always a right…

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

A: 6-3i2+7i

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

A: 19--4

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: If the altitude and the base of a triangle were each increased by 2 cm, the area would increase by…

A:

Q: A number of the form iy is called pure imaginary ylgn İhi

A: True

Q: Find the positive angle less than 360 ° that is coterminal with a -1166 ° angle:

A: It is asked to find the positive angle less than 360o that is coterminal with -1166o

Q: Use de Moivre's Theorem to find the reciprocal of each number below. −2 x square root 3 − 2

A: By De-Moivres's theorem , if a number is represent by x, then we can represent its reciprocal by1x…

Q: Show that the product of a+ bi and b+ai always results in a purely imaginary number, given that a…

A: Show that the product of (a+bi) and (b+ai) is a imaginary number . Here a and b are real number.

Q: Consider a right triangle with a side of length x opposite angle A, a side of length y opposite…

A: Given that:    sinB=13x=6

Q: a+bi 26 19) Expressed in form, 2-3i is equivalent to

A:

Q: If the measures of the acute angles of a right triangle are 2x + 4 and 3x - 9 , then x = ___?

A: If the measures of the acute angles of a right triangle are 2x + 4 and 3x - 9 , then x = ___?

Q: Which of the following can be said to be completely NON related to finding the length of a segment?

A: Length of a segment: The length of a line segment joining two points is nothing but the distance…

Q: Which of the following can be said to be completely NON related to finding the length of a segment?…

A:

Q: The angle between 0° and 360° that is coterminal with - 1475° is

A:

Q: The Sun is 25 above the hori 2on

A: Given, The angle inclined by the sun which is above the horizon is θ=25° Height of the building:…

Q: Solve the following: Answer: tan285° UIS #31

A: Solve the given problem.

Q: The figure above is taken from Book IV of Euclid and is key to his construction of a regular…

A: There are many constructions of the regular pentagon, some of which use only the tools prescribed by…

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: In any obtuse triangle, the square of the side oppo- site vne obtuse angle is equal to the sum of…

A:

Q: A number of the form iy is called pure imaginary ylgn O İhi

A: A number of the form iy is called pure imaginary

Q: If sec 4θ = csc(θ+20), then θ is equal to?

A: topic - trigonometric identities

Q: Find the imaginary component if the nth root of  a + bi is determined for a = 9, b = 3, and n = 6.…

A:

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: in a certain right triangle ABC, angle B is the right angle, AC can be expressed as (2x+y) while BC…

A:

Q: What is the Pythagorean Theorem in deep detail?

A: Solution: The objective is to write the Pythagorean theorem

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: 9. The altitude to the hypotenuse of a right triangle forms two triangles that are similar to each…

A: Answer is True.

Q: Use de Moivre's Theorem to find the reciprocal of each number below. -2 square root of 3 -2i

A: We are asked to find the reciprocal

Q: I am given that tan θ = 3/5, so I can conclude that y = 3 and x = 5.Determine whether the statement…

A: Given: tanθ = 35  conclude that y = 3 and x = 5 To determine: Whether the given statement make sense…

Q: How can you be familiar with making a proof in geometry?

A:

Q: In an isosceles right triangle ABC, with the right angle at C, the length of a leg is 20 inches.…

A: If the length of the leg of a right isosceles triangle is x, then the length of the perpendicular…

Q: Use Demoivre's Theorem to find the fallowing- answer in Standard form. your 2 eis 20 Write

A: Given (√2 cis(9π/20))5 Using demoivre's theorem we can write Zn=rn cisntheta  =(√2)5 (cis5(9π/20))…

Q: What are all of the solutions for the equation 3cos(30) - 8 = -11 on the interval of [0°, 360°)?

A:

Q: 2 Suppose that 0 is an angle in standard position whose terminal side intersects the unit circle at…

A: Given,         Suppose that θ is an angle in standard position whose terminal side intersects the…

Q: Find the imaginary component if the nth root of a + bi is determined for a = 10, b = 8, and n = 7.…

A: Imaginary component of the function

Q: A right triangle has legs of length X, 2X +2, and a hypotenuse of length 2X +3. What are the Lengths…

A: Topic: triangle

Q: The formula for Pythagorean Theorem is a? + b² = c? %3D O True False

A:

Q: show that the product of a+bi and b+ai always results in a purely imaginary number given that a and…

A: The general form of complex number is :-       a+ bi , where a is real and b is imaginary part.…

Q: A number of the form iy is called pure imaginary ylgn O İhi O

A: given a complex number

Q: Are they congruent? If they are what are the corresponding parts and theorem? If they are not can…

A:

Q: (b) Show that ii is real, even though i or 5i is not.

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: Which irrational number is represented by point D?

A: In the question, it is given that some points are marked on a number line    We can see that the…

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: What is the formula of Pythagoras Theorem

A: