Suppose z = a+ bi, w = u + iv, and

Q: Let u = (9,3,-3), v = (0,2,-5), and w = (6,5,4). Compute v X w. vxW=(

A:

Q: E. Prove the following: 四- Iz.l 1.

A:

Q: If z = 1+ 2i and w = 3+ 4i, express the following in the rectangular form: (a) 2|w| +(1 – i)2² w + z…

A:

Q: Write 1/ (3 + 4i ) in standard form a + bi; that is, find the reciprocal of 3 + 4i.

A:

Q: 1. Find the value for a and the value for b such that au + bv = w if u=(-2,3), v= (1,–3), and…

A:

Q: Show that (u×v)· w = u ·(v×w).

A: As we know that, Multiplication is an Associative Property, i.e. (a x b).c=a.(b x c) and Sometimes…

Q: Express the product of 9i5(2i³ - 3i16) in a + bi form.

A: 9i15(2i3-3i16) =(9i15)(2i3)-(9i15)(3i16) =18i15+3 -27i(15+16) =18i18 - 27i31 Now i=√(-1) i18=-1…

Q: iF Uo=c Unı%=D(2n+2)Un +2 n+ Find Un

A: Use the given relation.

Q: 2. 4 7 X•w Compute w • w, x•w, and using the vectors w=-1 and x = w•w - 5 3 w•w = (Simplify your…

A:

Q: 3. Find the positive value of real parts of the possible values of z that satisfy the equation: zz +…

A:

Q: for z=1+5i and w=3+i, find z/w Write the result a+bi

A:

Q: Suppose that u × v = ⟨1,0,4⟩. Find (2u−3v) × v.

A:

Q: If Z = 2 + 5i, write down the conjugate of Z. Multiply Z by its conjugate and write answer in the…

A:

Q: Question 3 of 5 Simplify as much as possible. V2y-y50y v2 Assume that all variables represent…

A: Given expression is:Factoring the terms to apply the square root:

Q: Show that if PER"×" is an orthogonal projector, then P+ = P.

A:

Q: If u = 7i - 2j + 3k and v = -i + 3j +5k then Projuv is a- 62 62 10 b- +j+k 35 35 62 10 d-i+j+k 35 35…

A: Given vectors are, u=7i^-2j^+3k^  and  v=-i^+3j^+5k^ Now projection of v on u is given by.…

Q: give vector form for the solution

A: Here we have to find the vector form

Q: When 3+4i / 2+i is expressed in the form a + bi, what is the value of a?

A:

Q: If u = 2i + 5j; v = i - 2j; w = 3i - j, so u + v * w is:   -3   3   6 -6  9

A: Given that: u = 2i + 5jv = i - 2jw = 3i - j To find: u + vw

Q: Determine whether b can be written as a linear combination of a, and a2. In other words, determine…

A:

Q: If u = 2 + i and v = 2 - 2i, then what would be the result of the following combinations in the form…

A: We know that complex numbers are of the form z=a+bi where a is real part and b is imaginary part.…

Q: Determine whether b can be written as a linear combination of a₁ and a2. In other words, determine…

A: Please refer to the solution in next step.

Q: 3.10. Rotate the vectors by 30%. *:[],三闾

A: We have to Rotate the given vectors by 30°.

Q: Q) Verify that (bx с) %3D b.(с х а) — с. (а x b) if a %34i — 3ј +6k , b- 5i +4j — 3k, с %3 4i +6j +3…

A: Given the three vectors

Q: If 2-a-5i/(1-bi) = 3 - 5i, find a and b

A:

Q: Please explain properties or rules for each step

A:

Q: 4. Show that any complex number of norm 1 (except -1) can be written in the form z = (1 + it)/(1 −…

A: We have to prove that any complex number of norm 1 (except -1) can be written in the form…

Q: If u = [3, - 1] and v = [1,4],compute and draw u + v.

A:

Q: Given that (1+2i)² = a + bi, correctly complete the following: • a equals [ Select ] [ Select ] b…

A: