prove it :     ( 1/2 + 1/2i )10 = 1/32i

Q: Evaluate: Ei°(3n + 7) = [ ? ]

A:

Q: Find the principle root of 8/. (A) 8i = 3 +1 (C) V8i = 3 + 2/ (B) V8i = 23+1 (D) V8i = 2/3 +8i - %3D…

A:

Q: Solve for a: 63I+7 _ 36219 T =-25 Or=-11 Or 16 O=25

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Q: 1. Simplify: a. 2i68 – 3i-89 + 4i114 i-125 + 2i213 + 3i-314 b. 5i97 - 4195

A:

Q: 4. (a) (i) Calculate (4 + 6i)².

A:

Q: 1.) Find the indicated sum. 3 4i = i= 1

A: Answer is- 24 Explanation is given below...

Q: 7- The indicated power for (1+ i)20 by using De Moivre's Theorem is

A: Given: 1+i20 we compare, 1+i=x+iy we get, ⇒x=1 &y=1 Therefore, r=x2+y2r=1+1=2r=2

Q: 5. e-1+4i 5. cosh(2e3')

A:

Q: Which of the following expressions is equivalent to 2i? Select all that apply. a (2i) (2)

A: Given: x23 Now check:   a)  x32=x132=x13×2=x23 b) x3=x123=x12×3=x32 c) x2x3=x2-3=x-1 d)…

Q: 11 > 5i2 + 4 i=1

A:

Q: Convert 6i to the form x + iy

A: See the answer below

Q: Express 8 - 4i in exponential form reże, where is in radians to 3 decimal places, and in the range 0…

A: Introduction: Complex numbers are represented in polar form as the complex number's modulus r and…

Q: a) Find the square root 14+ 4√6. b) If ƒ(r) = (2+1), show that ƒ(r) — ƒ(r+1) = r(r+1}(r+2). Hence,…

A: B. f(r) - f(r+1)

Q: Visualize the addition of (3 + 6i) + ( – 7 – 8i) by plotting the initial point, and the result. 10+…

A:

Q: 1. Find the (2i+1) i=0

A: We have to find the value of ∑i=05(2i+1)For this, we will substitute i=0,1,2,3,4,5 and apply…

Q: Find the product. (3 + 4i)(4 − i)

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Q: Find (root3 / 2 - 1/2i)30 by the de moiver's formula.

A:

Q: 18. Express the following in simplest form: (3+ 4i)?(3 – 4i)²

A:

Q: ); Find the value of 7 if e =1+3i %3D

A: Here just to use the any complex number can be written as reiθ

Q: Fill in each blank so that the resulting statement is true.

A: Given:∑(5i+3)i=117 To find: The first three terms of∑(5i+3)i=117 and their common difference.

Q: 1.047i 4Q. Using De Movier's Theorem find all roots of √/25 e¹

A: The given problem is to find the all roots the given complex expression by using De Movier's…

Q: 9 – i 3 + 9i If A = find A*. 7+ 5i -4 + 8i ( ) ? ? ? ? A*

A:

Q: Find the value of i20 + + 2i².

A:

Q: 2) Σ=1 (2i – i3)

A: ∑i=1n(2i - i3 ) 2∑i=1ni - ∑i=1n i3   here we use formula  ∑i=1n i = n(n+1)/2 ∑i=1n i3 = n2(n+1)2/4…

Q: Use DeMoivre's Theorem to find the following. Write your answer in standard form. -8 – 8i3 8+8i -16…

A: Explanation of the answer is as follows

Q: | 2+4i -3 il %3D

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Use the method of difference tables to find a closed formula in terms of n for the > i(2i – 1).

A:

Q: [(5+ 2i)(-1+ 4i) – 5260°]*

A:

Q: Express the following in a + ib form a. (4i-7)+(2+i) b. (5-2i)(2+ 2i)

A:

Q: AS: の4+o4i (3-i)(I-2i) (2+i)(1+2i)

A:

Q: n Compute (2i? – 7i) = i=1

A: ∑i=1n2i2-7i

Q: Using de Moivre's theorem to compute (−1−√3i)^11 we find that the answer is?

A: For any complex number x and any integer n, r ( cos ⁡ θ + i sin ⁡ θ )n = rn (cos ⁡ ( n θ ) + i sin ⁡…

Q: that is an ei -1

A:

Q: cos" (1 + 2i) O 1.9372 + 1.7552i O 2.1372 + 1.2252i O 1.8858 - 1.3347i 1.1437 -1.5286i

A: Evaluate the value cos-1 (1+2i). Write the complex number is given as rectangular form z = a + i b.

Q: Find A*. 8i 1- i A = 16 3+i 2+i x - (; ; ) ? ? ? A* = ? ? ?

A:

Q: 6) Find all values of 0 such that 360° seS720° and sin e

A: Given that    sinθ=-513   , we have to evaluate θ where 360° ≤ θ ≤ 720°  We first find in which…

Q: Find the first 4 terms given the (si: 1. 1, = 3n- 14 %3D %3D %3D

A:

Q: Let A = |'5 [1-7i 1+4i Find A 31 - 7i 5 l1+ 4i 3il + 7i li – 4i -3il 5 (b) (0) [' ;" + 7i 1-4i - 7i…

A:

Q: Express sinh (i) in the form a + ib

A:

Q: 1. Solve and sketch the 4 answers to x - 16i TO

A: Given, x4=16i

Q: 2. i 3-2i 5

A: We have to compute the indicated power -i3-2i5

Q: 109. Find a value of N such that /4 tan x dx < 10-4

A:

Q: Find all values of the full power. ASAP 2 (ei)√₂

A:

Q: 8. Given 0° <0 < 360°, solve 8 tan 0 = 0. 90°, 270° 0°, 180° O 0° 90°

A: We will find the solution in the following step

Q: Show that x = 2 + 3i is a solution to the equation x- 4x + 13 = 0.

A: Given:       Quadratic equation  x2-4x+13=0       x=2+3i    this is in the form of ax2+bx+c=0…

Q: Find the distance d between z1 = (-7– 6i) and 22 = (-15 – 12i). %3D

A:

Q: Use Euler's formula to write the expression e3+8i in the form a+ib. Round a and b to four decimal…

A: We have to solve given problem:

Q: 2. V16230° 3. In(-1 – i) 4. In(4i)

A: The rectangular form is z=a+ib