Applying De Moivre 's theorem in writing the complex number (-1-i)* in the form a + bi, the value of a is and of b is

Q: Let z is a complex number and Z is the conjugate number of z then () equals O a. z1 Z2 b. 21 Z2 C. O…

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Q: Determine the absolute value of the complex number z = -1 - 2i.

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Q: Let a = 1+bi be a complex number, b>0, such that a is a real number. Evaluate 1+a+a² + . + a". ....

A: Given a complex number : a=1+bi where b>0 It is given that  a3 is a real number. We need to find…

Q: N=-7+1li %3D

A: Given complex number Z=-7+11i

Q: Represent the complex number geometrically.2i(2 + 3i)

A: given 2i(2+3i) =4i-6=-6+4i It is represented in a complex plane. where x-axis represents real value…

Q: Write the complex number in polar form with argument 0 between 0 and 2n. 7 - 7i

A: The expression of the polar form is given by z=rcosθ+isinθ Given complex number is (x+iy)=7-7i. The…

Q: Express the complex number z =1- 3i in the form of ree and deduce the following complex numbers in…

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Q: Express the complex number in exponential form z=rei*theta *-2pi(i) *2/(1+i)

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Q: Use De Moivre's Formula to compute the three complex cubic roots of v3 + i. List your answers in the…

A: To find: complex cubic roots of given complex number.

Q: Write the product of complex numbers in the form a + bi. (3 + 3i)(2 + 4i) =    (6 − 2i)2 =…

A: I²=-1

Q: Use De Moivre’s theorem to change the given complex number to the form a + bi, where a and b are…

A: Given: Let z=-1+i8  To Find: To change the given complex number into a+ib form using De Moivre’s…

Q: Determine the four fourth roots of the complex number Z 3-4j, using De Moivre's theorem and express…

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Q: Two complex numbers z1 and z2 are given by z1 = 3 + 2i and z2 = − 1 − 4i. Evaluate, (a) |z1z2| (b)…

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Q: Simplify the complex number z=j(-1+j). Then, find the modulus of the complex number z and the…

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Q: Use De Moivre's theorem to change the given complex number to the form a + bi, where a and b are…

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Q: Use De Moivre’s theorem to change the given complex number to the form a + bi, where a and b are…

A: Given that, 2+23i10

Q: 11. Write the quotient of the complex numbers in the standard form z=x+ iy. 3+i 1-2i

A: If you like the solution then please give it a thumbs up.... The Answer is:           Standard form…

Q: Find the midpoint between the pair of complex numbers. (-5 - 8i) and (-3i) O 2.5 + 2. 5i O-2.5 5. 5i…

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Q: 3. Determine all complex numbers z for which |2z – 1| < 2|2 – i|.

A: The given problem is to find all the complex numbers that satisfies the given complex inequality.

Q: Writing the 4th complex root of the complex number z*=i in the form a+ bi, the value of a is and of…

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Q: The conjugate of complex number z satisfy: z-z=2ilmz O z+z=10 - z+z=2Rez O - z-z=00

A: The complex number, z is usually represented as z=x+iy . Here, x is the real part and is represented…

Q: Applying De Moivres theorem, the following represent the complex number ( –1-/3i)' in the form a+…

A: Given :

Q: Represent the complex number geometrically.4(-1 + 2i)

A: 4-1+2i

Q: Simplify the complex number z and express it both in rectangular and polar (A) .form (3 + j6)(6+ j4)…

A: Now, we have to simplify the given complex number and express it in rectangular and polar form.  The…

Q: Use De Moivre’s theorem to change the given complex number to the form a + bi, where a and b are…

A: Given: Let z=1-3i3 To Find: To change the given complex number into a+ib form using De Moivre’s…

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: Writing the 2nd complex root of the complex number 25= - 2/2i in the form a+ bi, the value of a is…

A: According to the De Moivre's Formula, all nthroots of a complex number  r(cos(θ)+isin(θ)) are given…

Q: What is the algebraic form of the complex number 13 e 12+5i 5-12i 12-5i 5+12i

A: We will use the basic theory of complex numbers to answer this question.

Q: Z = (1– j)!-2j

A: We have to find the real and imaginary part of the complex number Z=1-j1-2j. So we have to write Z…

Q: (A) Simplify the complex number z and express it both in rectangular and polar form. (3+ j6)(6+ j4)…

A: Given that z=3+j66+j42+j1j2+7+j10 express it In rectangular form and polar form

Q: Show that the complex number z = −1 + i satisfies the equation z2 + 2z + 2 = 0

A: we have to show that the complex number z=-1+i satisfies the equation z2+2z+2=0

Q: Let z be a complex number such that z, z3 and z5 form an equilateral triangle on the complex plane.…

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Q: Use DeMoivre’s theorem to find z4, if z is 1 + 1i. Express your answer in complex form

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Q: Writing the 2nd complex root of the complex number z=- 2/2i in the form a+ bi, the value of a is 0…

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Q: 4i Rewrite the complex number 10e“ in a + bi form a b = II

A: We have to write the complex number 10e4i in a + bi form.

Q: Find the distance between the pair of complex numbers. (7 - 2i) and (5 + 8i) O4/26 V194 O2/2 2/26

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Q: Applying De Moivres theorem, the following represent the complex number (-1-V3i)' in the form a+ bi.…

A: To represent the complex number -1-3i7 in the form a+bi by applying De Moivre's theorem.

Q: Writing the 2nd complex root of the complex number =- 2/2i in the form a + bi, the value of a is zi…

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Q: A complex number is graphed as a point on the complex plane below. 2- 1 Real -3 -2 -1 -10 (0, -1)…

A: To determine: The complex number is graphed as a point in the complex plane. Given information: The…

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: Use De Moivre’s theorem to change the given complex number to the form a + bi, where a and b are…

A: Consider the given expression as -32-12i20

Q: (A) Simplify the complex number z and express it both in rectangular and polar form. (3+ j6)(6+ j4)…

A: To express: The complex number in rectangular and polar form. Given: The complex number is…

Q: Find all complex numbers z satisfying = -i

A: i = -1(i)2 = -1

Q: p and q are complex numbers such that p| = x + 2, |q| -žx – 1, and |p+q] = 2x + 4 %3D On what…

A: I have provided solution in step2

Q: Use De Moivre’s theorem to change the given complex number to the form a + bi, where a and b are…

A: Solution: Consider the given complex number is: z = 3 + i7 We have  z = a + ib⇒z = rcos θ + i sin θ…

Q: Use De Moivre’s theorem to change the given complex number to the form a + bi, where a and b are…

A: Given complex number is: Let us consider, r cos θ=22r sin θ=-22 Then we get,…

Q: Let z be a complex number. Then e32+ is bounded over the set of complex numbers. a. True b. False

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Q: Use De Moivre’s theorem to change the given complex number to the form a + bi, where a and b are…

A: Given complex number is: 22+22i25 Let us consider, r cos θ=22r sin θ=22 Then we get,…

Q: Let z2 = -V2 + i/3, w = -3+ 3i and p= -3– 2i. 1. Find all the complex numbers given by In z2.

A: It is given that