T= -1 + √√3i 5 + 4i 0

Q: WORKSHEET 3: Multiply and simplify. (√3 + 1) ( √3 – 1) (4-√7)(4+√7) 20 3- (√27-2)(√27+2) |

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Q: Differentiate y with respect to x given y = √x(2+bx³) 7bx3+2 2√x 0 36х 2 6bx+2 Vx 6b5x+1 2

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Q: Differentiate implicitly 14. 4√x – 8√y = 6y²

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Q: Use De Moivre's Theorem to find (-2-2√3 i)². Put your answer in standard form.

A: Step 1Complex number has two basic forms, one is rectangular form and other is polar…

Q: Find the rational roots of equation: 3y³+5y²+8y+4

A: We have fy=3y3+5y2+8y+4   We have to find rational roots of given equation fy=03y3+5y2+8y+4=0…

Q: Multiply the following. (5x° + 8y) (5x³ - 8y) (5x3 + 8y) (5x3 - 8y) = (Simplify your answer.)

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Q: Q3: Express complex numbers to polarform and draw them: 1. 5+2i. 2. 4i

A: As we know that we can represent a complex number from rectangular to polar form as :- Rectangular…

Q: √128x9y12217

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Q: V16 – V-36 v25 +v-16

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Q: Find the change of variable x = Py that transforms the quadratic form x' Ax into y' Dy as shown. 2 −…

A: Matrix A is of quadratic form ( from LHS) and D be diagonal matrix of eigen values (from RHS)…

Q: Find a - b

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Q: Simplify: а) (4 — 3) + (6 + 25) e) (5 – 3i) – (-8+ 7i) f) (4 – 2i) (3 – 5i)

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Q: x+2-√√a x=3 = √√√x x-6

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Q: x Q3: Show that csch-¹ (²7) = coth-¹(x+¹) x-1,

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Q: Express ½ (1 -  √ 3i). ANS: cis 3000

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Q: √2-1/2 is irrational

A: We need to find whether irrational or not.

Q: √(3+4i)=A+Bi, find A and B

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Q: 2-VTO 3+VTO Simplify to its principal root.

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Q: Integrate: /25 - x8 √√25 x5 - dx

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Q: Which of the following are the solutions to the polynomial equation x - 13x +36 0? O a. x = 0, 4, 9…

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Q: Q1- If z₁ =3+2i, and z2 = 1-2i. Fined the real part and imaginary part of the 2z2-z₁+5-i following…

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Q: y = (2x+5) (x-4) y = (4x³- 5x)³ 11. y = 10. ƒ(x) = 2x-1 x+6

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Q: dx Compute√2+16 dr

A: Steps and explanations are as follows:In case of any doubt, please let me know. Thank you.

Q: 9- Find 5√10 – 3x² dx

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Q: 1. S(√t -√√² + √√³) dt

A: solution ) ∫ ( t - t2 3 +t35 ) dt = ∫ ( t1/2 - t2/3 + t3/5 ) dt  we know that  ∫xn = xn+1/n+1  = (…

Q: Express the formula in terms of f R T Simplify 1/8a³b³. : f+p f-p 1 =—= a¹b² × (16√√a4f6)-1/2 25…

A: As per the company rule, we are supposed to solve the first three sub-parts of a multi-part problem.…

Q: d da earctan(√2)

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Q: Find wa+bi = √ where a and b are real numbers. - -60i - 11

A: We have to find

Q: 2. Simplify completely: (a) √1+i√3

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Q: Calculate: 1 √√√√x (2√x + 5) √x+5 dx

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