Find the indicated power using De Moivre's Theorem. (Express your fully simplified answer in the form a + bi.) (1 - i)18

Q: 4. Find all the roots for the equation, z5 = -3+ 3i in the form of a + bi. %3D

A: Concept introduction: De Moivre's formula The nth roots of a complex number a=rcosθ+isinθ are…

Q: Find the square roots of the complex number z= 16 (cos 60° + i sin 60°). There may be more than one…

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Q: z1 = -2 – 2/3i, z2 = 5i

A: z1=-2-23i,  z2=5i Now, z1=-22+-232=16=4 & argz1=θ1=tan-1yx=tan-1-23-2=tan-13=π+π3…

Q: Find real numbers a and b such that the equation is true.a + bi = 10 − 5i

A: A number of the form a+ib is known as the complex number. Here i  is known as the imaginary unit. A…

Q: 5. Simplify to a C. Write answers in the form a + bi a, beR (g) (1+3i)(1 – 4i) (h) (5 – 2i)(-1+ i)…

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Q: 2) The complex conjugate of z is denoted as z. Solve for z in the equation: z - 12 = j(9 – 2z)…

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Q: 3. How may the following complex numbers be obtained from z = x + iy geometrically? Sketch. а. 2 b.…

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Q: Solve for z, and give your answer in the form a+bi. z/(3+2i) = z+4−5i

A: We will find out the required value.

Q: The ________ ________ of the complex number z = a + bi is z = r(cos θ + i sin θ), where r is…

A: z=a+ib be any complex number

Q: 7. Find the four roots of the equation z* +81 0. Write the roots in the form a + bi. 4

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Q: 3) The complex conjugate of z is denoted as z. Solve for z in the equation: 27(1– j2) 2 - j3 j 1+ j2…

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Q: Solve for z, and give your answer in the form a+bi. (z-2-2i)/(-5-i) = z

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Q: Find all solutions of the equation and express them in the form a + bi. x2 + x + 1 = 0

A: Given :                        x2+x+1 = 0          Use quadratic equation,…

Q: The complex conjugate of z is denoted as z̄. Solve z in equation: z-12=j(9-2z̄) giving the answer…

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Q: Develop a quadratic equation in x for the data point depicted as follows: (1,10), (4, 13), and…

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Q: Given the complex-valued function 1+z z² Evaluate f (¹) (A) -4-3i (B) - f(z) = (C) −¹+²i (D) none of…

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Q: Given that z1 =1– 2i, z2 = -3+4i. Z1 Find , and express it in a+ bi Z2 form.

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Q: #20. USE TRIGONOMETRIC FORMS TO FIND z1/z2 а. z1 = -1 + i, Z2 = 1 + i 2, i b. z, = V3 – i, z2 = - V3…

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Q: Q3) Find complex root of the z³ = -27, k = 0,1

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Q: Use de Moivre's Theorem to find the following. Write your answer in standard form. (−2√3+2i)4

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Q: Let z = -4 + 3i and zw = -7 – 2i. By showing clear steps, find w in the form of a+bi.

A: Given:        z=−4+3i,  zw=−7−2i

Q: 1. If z = 1+ iy is a complex number. Use the exponential form to compute (1+ /3 i)201

A: Definition used -            DeMoivre's theorem -             For a complex number z=r(cosθ+isinθ)…

Q: The polynomial z* + 3z? + 6z + 10 is denoted by p(z). The complex number -1+ i is denoted by u. (i)…

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Q: V3 1 (- 2

A: given(-32-12i)20 =(-1)20(32+12i)20 =(cos30+isin30)20 The formula of Demoivre's theorem is cos θ+isin…

Q: e the complex number 8e" in a + bi form X error - invalid form

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Q: To prove the equation a +a - 1=0 has exactly one real root, which of the following theorems should…

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Q: Find the product of – 2 + 1i and its conjugate. The answer is a + bi where The real number a equals…

A: The solution is given below:

Q: Let z = -4 + 3i and zw = -7- 2i. By showing clear steps, find w in the form of a+bi.

A: Given  z=−4+3izw=−7−2i

Q: . Let z = -4 + 3i and zw = -7 – 2i. By showing clear steps, find w in the form of a+bi.

A: In this question , the value of z is inserted into zw=-7-2i, and then it is solved for value of w.

Q: 3) The complex conjugate of z is denoted as z. Solve for z in the equation: 27(1- j2) j 2-j3 1+ j2…

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Q: 2) The complex conjugate of z is denoted as z. Solve for z in the equation: z – 12 = j(9 – 2z)…

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Q: Find all solutions of the equation and express them in the form a + bi.

A: Consider the given equation x2+12x+1=0. Simplify the given equation. 2x2+x+22=02x2+x+2=0

Q: Find all solutions (real and complex) z in Cartesian form (a+bi) to the equation rº –9r+8 = 0.

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Q: Find the distance d between z1 = (8+ 8i) and z2 = (-8+ 8i).

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Q: To prove the equation a + * – 1 = 0 has exactly one real root, which of the following theorems…

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Q: C. Find all complex numbers z of the form 2=x+y such that that zz = 25 and *+y = 7.

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Q: (-√3+i)^4 Use de Moivre's Theorem to find the following. Write your answer in standard form.

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Q: 3) The complex conjugate of z is denoted as z. Solve for z in the equation: 27(1- j2) j 2- j3 5z 1+…

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Q: The complex number z is given by Z = z²+1 a²-b² 2z a² + b² a+bi a-bi show clearly that

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Q: Given that Z1 =1– 2i, z2 = -3+4i. Find and express it in a +bi Z2 form.

A: As per our guidelines, we are allowed to answer only one question. Since you have asked multiple…

Q: 2) The complex conjugate of z is denoted as z. Solve for z in the equation: z – 12 = j(9 – 2z) %3D…

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Q: Find the distance d between 21 1 = (-7- 6i) and %3D z2 = (-15 – 12i). %3D

A: z1=-7-6iz2=-15-12i We can say that the co-ordinates of two points are (-7,-6) & (-15,-12).…

Q: ) The complex conjugate of z is denoted as z. Solve for z in the equation: 27(1 – j2) 2 - j3 5z 1+j2…

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Q: Suppose z=2- 3i, What is a complex function f (z) =-3z - 2i Re (z) ? | | o 6-13i o-6-13i o 6+13i…

A: Anu complex number z is of the form z = x+iy, where x and y both are real number and i is square…

Q: (c) 1(3-iz)리 on l리<1 (d) 15 + 2iz리 on |리 < 1

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Q: a) Express the complex number Z 10 (cos 150° +i sin 150° ) in rectangular and exponential form. V3…

A: (a)z=10(cos 150°+i sin 150)where r=10and θ=150*π180=56πExponential form is z=reiθz=10ei5π/6In…

Q: A. Find the indicated power using De Moivre's Theorem. Leave the answer in the form a + bi. 6. +

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Q: c) By using De Moivre's theorem, find (3/5 – 3i) in the standard form.

A: To find complex no. in standard form using De Moivre's theorem .

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.