2 If the time. =1 moves in Such wery 1-12 + ²√2 = 1/², where c is a constmit, then 92 b Prove that the foot of the peopendicular from the Origin on the straight line describes the x² + y² = C с that a

Q: Use de Moivre's Theorem to find the following. Write your answer in standard form. (√2 cis 77)

A:

Q: If z1 and z2 are complex numbers such that |21| = |2|, prove that arg(2122) = arg ((21 + z2)²) .

A: This  problem is related with complex analysis. Given that z1 and z2 are two complex numbers such…

Q: from x = 2 to x = 10 and x; is any value of x in Ex¡. Express lim s as a definite integral. n-x n D…

A:

Q: 5olve The simultaneaus.equation 22 tiw - 2 2+ (1ti)w =3;

A: Given :                    2z + i ω = 2 .................(1)2 + (1+i)ω = 3i ..............(2)then we…

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: show IBat = (at 5) (1+i) (a+bi where 9,6 Are reals Hense tEs Find the value 2 (9-31) (a43i) 15-51)

A:

Q: 2) evalu ale the following integrals 3) ure completing up the square Nx2 - 2n - 2 b) shew that 3x +…

A: As per the guidelines I am supposed to do the first question among multiple questions. But for your…

Q: Assume that y represents a positive real number. What is the conjugate of Vy - 24?

A: y-24

Q: Find 8, if 360 <8 < 720° and cac (8) 2,3 3 EVE and& in QIL

A:

Q: IN! Write each complex number in standard form. 4 10. 25 Choices for 10-16: 1 A) 11. B) C) -- 49 D)…

A:

Q: Let (zn)n≥1 be a geometric progression of complex numbers, and suppose that z3 = −1 and z5 = 7. Find…

A:

Q: 0.78125ab²1 9 112, 15 ² q. (3/8c²d¹²e" 2 -2 S. (6; ²K³) ²x 20K 1³ X 3₁1-3 (3) = P. (4a² b ²) ²³² × 3…

A: According to guideline given to us, in multiple question we are only allowed to answer only first…

Q: 9. For which complex numbers is it true that z² = |2|²?

A: Here is the solution:

Q: Prove the following:  tanxsin 2x=2sin2x…

A:

Q: Evaluate L, sinh 3t (3

A: L13sinh3tUse the constant multiplication property of Laplace Transform:For function ft and constant…

Q: is an imaginary root of unity. Prove that (1)(a + bo+cal) + (a + but co? 50 - (2a-b-c) (2b-a-c)…

A:

Q: c) Let k EN be odd, show that (1+i)2k + (1 – i)2k = 0 d) Using Demoivre's theorem, show that, if z =…

A: This Question Contains the multiple part.  For (b) we will use the principal of…

Q: 3) Find all the roots of the following equations z = √1-i 14 b) c) Z - i z = z = 964

A: a)

Q: Fibonacci Numbers: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ... Define the Fibonacci sequence {f}…

A:

Q: Find the SUM of all the complex zeros of f(x)= x3 + 3x2 + 7x + 10 a.) -1  b.) -2  c.) -3  d.) 0  e.)…

A: It is given that

Q: If a and b are complex numbers, prove that |a+b|<\a|+\b| .

A:

Q: 18) Find a + b, 2a + 3b, |a|,  and |a - b|.  a = 2i - 4j + 4k, b = 2j - k

A: The objective is to Find a + b, 2a + 3b, |a|, and |a - b|.

Q: Let ā = 6i – 5j and b 4i + j. Find a :

A: Here I am attaching image so that you understand each and every step.

Q: 3. Prove that the cube roots of 1 are given by -1+i√√3 =3 2 || 2 -1-i√√3 w³ = 1. 2

A: DETAILED SOLUTION IS PROVIDED BELOWExplanation:

Q: Find lul, Ivl, 12ul, · 121.14 lu+vl, lu- vl, and lul - lvl. u = (1, -3), v = (-4,-4) lul=√10 |v1 =…

A:

Q: Use Bombelli’s approach to find a complex number c = a + bi such that c3= 18 + 26i where a and b are…

A:

Q: Which of the following yields the value 3187 (8r+7y)dudy (8r+7y)dydr (8r+7)dudy O none of the oices

A: