Represent each of the following on an Argand diagram  i) Z1= -5 + 3i,  Z2= -1 + 7i   ii) Calculate│Z1+ Z2│

Q: If v = 5i + 4j and w = 6i - 9j, find 4v - 2w.

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Q: Solve for u. (u+3)² = 2u²+u+15 If there is more than one solution, separate them with commas.

A: Solution:-

Q: a. Show that If 1 iv3 z = 2 2 Then z7 = z. b. Evaluate all the roots of the Equation: z* + 16 = 0

A: We will solve both the parts only using some basic knowledge of complex numbers and their…

Q: Verify (a × b) × c = (a ∙ c)b − (b ∙ c)a if a = 4i + 2j + k , b = 2i − j + 7k and c = 2i − 2j + 3k

A: Given that a = 4i + 2j + k , b = 2i − j + 7k and c = 2i − 2j + 3k To verify  (a × b) × c = (a ∙ c)b…

Q: ii) Find the dot product of the vector a in part (i) with the displacement vector AB such that…

A: Given that  Following vectors  To find the dot product

Q: Solve the following lin dar System ",- Uz + U,- Mq M, t Ug t Wu 4v,-4%, +hu, - 2x, + 2n,- 2ng thy =…

A: x1-x2+x3-x4=4x1-x2+x3+x4=04x1-4x2+4x3=4-2x1+2x2-2x3+x4=-3

Q: Let a = - 4i – 33+ 3k and b = 4i – 33+ 2k. Find a – 36.

A: given   a→=-4i→-3j→+3k→    and  b→=4i→-3j→+2k→ we have to find a→-3b→

Q: Solve the first order PDE -2и, + 6и, — 0, и (4у, у) — 2у + 1

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Q: Question 1.) Q R. 2x-16 15у-10 3x+9 Бу+90 T. Find the Value of x and y.

A: Given: To Find: x=?, y=?

Q: Determine C if u=v=O (20 — 5и + 3)du - (20 + 4и — 6)dи %3D O 27 L- C

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Q: c. Show that(cscx) -1 xVx2-1

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Q: a. Write (-3, 5) in terms of i and j. b. Given w 6.2i – 3.4j and v = -1.7i + 2.2j, write 3w – 5v in…

A: It is known that a vector is a quantity which has both magnitude and direction. Now, a vector can be…

Q: If z, = 12 +5i and z, = -5-3i then find: Z2 2- zzlz -I Z2 3.

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Q: If v = 7i + 3j and w = 4i - 5j, find 6v - 3w.

A: Given v=7i+3j and w=4i-5j We have to find 6v-3w. 6v-3w=67i+3j-34i-5j=42i+18j-12i+15j=30i+33j

Q: Suppose ū=i- j, v = −2i + 4j+3k and w = -5i + 4j. Compute the following values: |u| + |v|=| |-6u|…

A: Since you have posted a multi subparts question according to guidelines I will solve first(1,2,3)…

Q: 6.1 Calculate the order of the element a) (4,9) in Z18XZ18- b) (7,5) in Z12×Zg. c) (8,6,4) in Z18×…

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Q: Determine the values of a, b, c and d: (1+ 2x)a = 1 + bx + 24x° + dx3 + 16x4 ax2 + bx + c = 0 -b ±…

A: Given,(1+2x)a=1+bx+24xc+dx3+16x4

Q: Let à = 27 - 5j + 4k and b = − − 5j + 4k. Find -a + b. -ā +b =

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Q: Eliminate the arbitrary constant C, and C2 of the equation: y= C;e" + Czeo O 2y" - – 6 – 0 O N – 2y…

A: Please check the options. Note: Given options does not contain correct answer. Given y=C1e2x+C2e3x…

Q: Find the value of X and Y in given that; 1 - 2y 4 7 2 2 - 2x 4 - 5 I3D 3. 2.

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Q: Let Z₁ Z1 If = 22 m= n = F/1, and Z₂ = -3-4i, -40 +-=-5 i, calculate m and n: n

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Q: Let a = - 5i + 33 + 2k and b = - 4i – 3 + 4k. Find a x b. ä xb = k

A: Cross product is the binary operation on two vectors in three dimensional space. It again results in…

Q: Determine Proy,b si ā = 3i– 4j+2k y b = -2i+3j-k

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Q: Let a = -27 +53 + 4k. Find a.

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Q: A pair of digits (a, b) is such that 4a5b32 is a multiple of 66, find a+b.

A: Please see the below picture for detailed solution.

Q: The formula in cell C2 is = A$2. Auto fill is used by dragging C2's auto fill box across to D2, E2,…

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Q: 1 2 A = 1 B 1 2 : , - compute AB 3 4

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Q: If a 10î + 10f + 5k, b = 5i – 2j – 14k, è = 4î + 7j – 4k , find the value of å x (b x 2).

A: The cross product of two vectors a=a1i+a2j+a3k ,b=b1i+b2j+b3k can be calculated using determinant…

Q: Find mJKL D 14x+3 L 14x +9 K

A:

Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.