Let yII + yI - 42y = 0 Find all values of k such that y = ekx

Q: [ 1 If A= -1 0 find x and y such that (xI +yA) = A

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Q: 4. Let z = -4 + 3i and zw = -7 – 2i. By showing clear steps, find w in the form of a+bi.

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Q: Determine all s ER such that i" - (i*)".

A: We have to determine all s∈ℝ such that ι4s=ι4s, where ι denotes the iota in a complex number. We…

Q: If x, y,z are integer's numbers and if x \ y then x\ z then: 1) Show that x\ ym - zn for m,ne z 2)…

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Q: Prove that Eo 2i = 2n+1 – 1 - i3D0

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Q: Which numbers satisfy lal = a? Which satisfy lal = -a? What about I-al= a?

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Q: 86. Show that Z, = r(cose + isine) and Z2 = r[cos(-6) + isin(-6)] are conjugates. %3!

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Q: 4. Let z = -4 + 3i and zw = -7– 2i. By showing clear steps, find w in the form of a+bi.

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Q: Let z1 = 4 (cos 7π/12+ i sin 7π/12) and z2 = 2 (cos 5π/12+ i sin 5π/12) Find z1z2. Find z1/z2

A: Recall:  z1z2=r1r2cos(A+B)+isin(A+B) z1z2=r1r2cos(A-B)+isin(A-B) We have, r1=4, r2=2, A=7π12,…

Q: 2. Find all number z such that Az" + Bz² + Cz = D a. A= 2

A: We'll answer the first question since the exact one wasn't specified. Please submit a new question…

Q: If x, y, z are integer's numbers and if x \y then x \ z then: 1) Show that x\ ym – zn for m,n e Z 2)…

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Q: [5] Determine the y(2021) of y=cos²

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Q: prove the identity  sin^4(t) - cos^4(t) = 2sin^2(t) - 1

A: We know that ,  sin 2 ( t ) + cos 2 ( t ) = 1  cos2 ( t ) = 1 - sin 2 ( t )

Q: ip Prove tan0 = e-ip 2i

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Q: х Prove that 1 < < sin x for all x e (0,5). - ド|N

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Q: 3 3 Prove that 2. j=l k=1 Ey =1 if ijk = 123, 231, or 312 Eyk -1 if ijk = 321, 132, or 213 Eyk =0 if…

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Q: 1 1. Prove the identity cosh2 r = 1 cosh 2x 2

A: As per our guidelines we are supposed to answer only one question at a time.  Kindly repost other…

Q: (2) Find all the numbers z such that elz = 10i.

A: Consider the given. eiz=10i

Q: Find all solutions of tan(3√x−5)=1 where k ∈ Z. (Notation: k ∈ Z simply means that k can by any…

A: Given:

Q: 5. Prove that if A and B are similar then dim(ker(A)) = dim(ker(B)).

A: We have to prove dim(ker(A)) = dim(ker(B)).

Q: Let gt): csc (U) for Oct C! and CSC 2- 13/2- 2 How do I find fogle)

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Q: ag show that: coth's =ţ he (xal/, X-1

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Q: 15. Let z = 2cos0 + i(1 – 2sin0) where -n < 0 < n Show that Iz – il = 2

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Q: Let Xvuniform(0,8) then E(x-2)

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Q: Prove Theorem (rA)T = rAT

A: Consider the matrix A=a11a12a13...a1na21a22a23...a2na31a32a33...a3n...............am1am2am3...amn…

Q: 7. Find a pair of integers (x,y) such that 4021x + 2014y= 1.

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Q: OFind all Max. , Min, seddle Point for the fure tiens below: 3xy - 15 X +.

A: We need to find max. min. and saddle points of given function.

Q: 7. (a) Find all the values of z such that e = 1+ i.

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Q: ,2 - 1 If z = cis 0, show that i tan 0. 22 +1

A: this is complex analysis question and also very lengthy questions so I can do it in advanced…

Q: limf, is measurable 00 ylan ihi

A: GIVEN a statement

Q: Find an explicit formula for s, if so = 1 and %3D Sn =2+2s0 + 2s1 +... +2s, 2+ Sn-1, Vn >1.

A: Generating Functions for a sequence a0, a1,a2,………an,……………… is an infinite series of the form ,…

Q: Prove that the inequality | cos(z)| 21- sin"(z) holds true for all z € R

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Q: two positive iontages and bare by 2, them prove that. (2° +1) is most divisible by (2²-1) let a with

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Q: O If z-frxy) show that つる

A: As per our guidelines we are supposed to answer only one question. For the solution of the problem…

Q: -Prove that: y" = 1 if y=csc(tan")

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Q: 3. Suppose csc(A) = where A terminates in QIV, and sec(B) = -3 where B terminates in QII

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Q: 1. Show that 0* = 0, I* = I. %3D

A: Matrix

Q: (*) 3. Let 2 = {A, |n = 1, 2, 3, ...}, where A, Find UN and N2, then !! %3D prove your conjecture.

A: We solve this problem using the basic properties of union and intersection. Also some basic steps of…

Q: Find a number z that satisfies: |z| - z = 2 + i

A: Complex number which satisfy |z|-z= 2+i

Q: リ この Shmo that e す。 are soluting of I

A: Note: Here, we will consider the differential equation y'''-6y''+11y'-6y=0....(1) instead of…

Q: Prove k den]=kaucn]

A: Given: To prove : k δn=k αnun

Q: Let T, >0 be given. S

A: Given,                      Tt=KTxx, 0&lt;x&lt;L, t&gt;0,                   ...(1)        T(0, t)=0,…

Q: Prove that (1+i)" + 1(1- i)" = 2m/2*1 nt cos 4

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Q: tan 4X Prove that 4t(1-ビ) if 1-6t +tf t=tan

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Q: alue of the funo 3) in the i

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Q: IRI- 2. <| sinz|< -e 2

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Q: 2 Verify the identity 4cos x (20 points) 2 2 2 4sin x cos²x + 4sin²x − 4sin³x = 4cos²x.

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Q: By expanding both sides of the identity (1+ x)"+4 = (1+x)"(1+x)* prove that ("**) - (") + «(,",) +…

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Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.