The variable z is often used to denote a complex number and 7 is used to denote its conjugate. If z = a + bi, simplify the expressions in Exercise. z? - ?

Q: How many complex numbers satisfies both equations, Iz- il = 2 and |z- 4i|l = 1?

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Q: Write the complex number in polar form with argument 0 between 0 ánd 27. 7/3- 7i

A: Given complex number z=73-i 7 We can represent complex number z=x+iy into polar co-ordinates rcos…

Q: What is the complex conjugate of 2 + 3i? What happens when you multiply this complex number by its…

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Q: Determine the non-zero complex number, z, that satisfies the equation: 37 = z.

A: According to the given information, it is required to find non zero complex number z which satisfy…

Q: Use DeMoivre's Theorem to raise the complex number to the given power. Express your solution in…

A: Compare the given complex number with the standard form and find x and y.Find theta using x and y.

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: 2. If a and b are complex numbers, and z is a complex number that obeys |z| = 1, show that az + b =…

A: Given that a,b and z all are complex numbers.   let, a=c+idb=r+is  and z=x+iy, where c,d,r,s,x,y all…

Q: Find the roots of the given complex number 1. z^3 = 2 – 3i

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Q: Find the roots of the given complex number 1. z^3 = -2

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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: Rewrite the complex number 9e2.54 in a + bi form

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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: 1-i10 Consider, z=1-i Now, z=12+-12=2 & θ=tan-1yx=tan-1-11=2π-tan-11     ∵The complex number 1-i…

Q: Express the complex number in trigonometric form with 0 ≤ θ < 2π.-17

A: Let z=−17⇒z=−17+i0The complex form z=x+iy in trigonometric form is written asz=rcosθ+isinθ,…

Q: Rewrite the complex number 8e" in a + bi form

A: The given complex number is 8e1i   Known fact eiθ=cosθ+isinθ

Q: In the complex number system, what is the value of the expression 16i* – 8i? + 4 ? (Note: i = -1)

A: Substitute the value of i and simplify the results.

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

A: Given :            -22 + 22i15   To change the given complex number to the form a + bi using De…

Q: If z is a complex number, show that the sum of z and its conjugate is a real number.

A: Given z is a complex number. Let z=x+iy We know that conjugate of a complex number is given by…

Q: If z is a complex number, show that the product of z and its conjugate is a realnumber.

A: Let z=a+ib be any complex number where a and b are real number. Then conjugate of z is z¯=a-ib

Q: If we write the following complex number in standard form (V3+ v13i)(V3 - V13i) = a + bi then

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Q: What is the complex conjugate of the root æ 3i? O a = -3i

A: if a+ ib is the complex then its conjugate root is a-ib

Q: what is the product of the complex number 3-4 and 8e53.13i

A: First convert 3-4i to magnitude and angle form then multiply to 2nd one. We get finally 40.

Q: Write the complex number in polar form with argument 6 between 0 and 2n. 9 + 9/3i

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Q: The complex number (0.866 + 0.5 i) can be written in the form of

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Q: Write the complex number in polar form with argument 0 between 0 and 27. -V6 + vzi

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Q: The complex number Z1 and Z2 are given by, Z1 = 3 - 5i and Z2 = -1+4i %3D Determine: 2Z1 +5Z2

A: topic - complex numbers

Q: Determine the equivalent complex number in rectangular form of the expression (-7 + 24i)2 (5 + 5i).

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

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Q: Evaluate (3+5i)(−2−2i)and express as a simplified complex number.

A: We have to evaluate (3+5i)(−2−2i)

Q: Find the imaginary component if the complex number a + bi is raised to m if a = 7, b = 7, and m = 6.

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Q: Given the complex number z such that z-4i = a+3zi , find the value of a if z is purely imaginary.

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Q: Find the product of the complex number z = 3 + 4i and its conjugate z*.

A: The complex number is given as z=3+4i

Q: Show that root of following quadratic equation are complex numbers a. 2x2 + x + 3 = 0 b. 7x2 + 5x +…

A: Compare the equation 2x2+x+3=0 with the general form of the quadratic equation ax2+bx+c=0, to find…

Q: 1. Write the complex number 2 + iv3 in the form of rete

A: We have to solve given problem:

Q: 1. Write the complex number 2 + iv3 in the form of rei0

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Q: Z is a complex number

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Q: Write the complex number in polar form with argument 0 between 0 and 2m. -VZ+ V6i

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Q: Find the real component if the complex number a + bi is raised to m if a = 5.6, b = 3, and m = 5.

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Q: If a, b, c, d are complex roots of x 4 + 2x 3 + 3x 2 + 4x + α = 0 and ab = cd, the value of α is…

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Q: Find all complex numbers z E C that satisfy the equation (7) + 3 = 0.

A: Solve the following

Q: 3. Given a complex number a + bi, the value of a is called the part. part and the value of b is…

A: Give query is to give the names of 'a' and 'b'.

Q: Express the complex number in trigonometric form with 0 ≤ θ &lt; 2π.12

A: 12+0i

Q: Find the four fourth roots for the complex number: v2 + v2i

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Q: 2. Write the complex number 3 + 5i 5 - 3i in the form a + bi.

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Q: Rewrite the complex number 3e1.5 in a + bi form

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Q: Find the roots of complex numbers. z5 = 4i

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Q: a. -16 + V-7 b. 47 ,601

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Q: How many complex numbers satisfies both equations, z – i| = 2 and |z – 4i| = 1?

A: We know that z=x+iy, then…

Q: Express the given complex number in polar form z=-5*square root of 3 - 5i)

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Q: Write the conjugate of the given complex number. -1 + 3i

A: Given query is to find the conjugate of the complex number.

Q: Determine the magnitude of the complex number, X. x-(8e(4ery

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