Let ABCDEFG be a regular hexagon. Show that 1/AB = 1/AC + 1/ AD.

Q: Simplify the complex number i .45 as much as possible.

A: See solution below

Q: z = tan¯1(4 – j7)

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Q: 1. Consider the equation (2¹ +64) = 32√√3³. Find all the roots and express them in rectangular form.…

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Q: (-19 – 5i) + (3 + 10i)

A: (-19-5i)+(3+10i)

Q: Plot the point corresponding to, z =2(cos30ο +isin30ο ) in the complex plane, and write an…

A: z = 2(cos 30° + i sin 30°)

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: state The Theorems in Algebra:- Caushy Lagrange

A: Cauchy's theorem (in algebra) Cauchy's theorem is a theorem in the mathematics of group theory,…

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

A: y-24

Q: 2. A single factor experiment was performed for 4 levels of the factor with 8 replicates. It was…

A: given y1¯=15 , y2¯=11 , y3¯=13 , y4¯=18 , MSE=4 two contrast τ1=μ1-μ4τ2=μ1-μ2-μ3+μ4 explanation…

Q: Let a = – 4i – 5j and b – 7i + 3j. Find a - b

A: we have  a→=-4i→-5j→ and b→=-7i→+3j→

Q: tain the principle root of JZ rectangular form 3-j4

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Q: Use DeMoivre’s Theorem to find all the cube roots of 2i. Show your work.

A: From the given z=0+2i. That is, a=1 and b=2. Recall the DeMoivre’s Theorem: "If Z=rcosθ+isinθ, then…

Q: Find a - b

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Q: Assume Z₁ = 2 - i and Z₂ = 1 + 3i. Find the product and quotient of z1 and 22. Z₁Z2 = Z1/Z2 =

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

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Q: culate √2-4i. Give your answer in a + bi form. In polar form, use the angle 0 < 2TT.

A: Topic:- complex number algebra

Q: Find the measure of 4x. 132° m4x=°

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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: Express answer in the form a​ +bi​   ​(2+4i​)^2

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Q: Find the measures of the angles of the triangle whose vertices are A = (- 2,0), B = (3,1), and C =…

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Q: 15x -10 X-8 3x-2 x2 -12x+32

A: