2. Write the given complex numbers in the form a + bi. 3 (a) 를 + 을-2유 (b) 2,0 + + 5i 5- 12i (c) 2-4i 3+5i (d) 3-i)(2+3i) 1+i į18

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

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Q: 2. Express the product of (3 - 2i) and (1 + 5i) divided by the product of (5 + 2i) and (-4 - i) in a…

A: Given expression is 3-2i 1+5i5+2i -4-i. Simplify the above expression as follows.

Q: 10 2) z = (-j)()

A: We have to use De Moivre's theorem cosθ+jsinθn=cosnθ+jsinnθ and Eular form of complex number…

Q: use the parallelogram law to form the sum and difference of the given complex numbers and then…

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

Q: Express the complex number z = 6 cis 180° in rectangular form a + bi. Select the correct answer…

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Q: (a) If z is a complex number such that z =8i, write z in the form a +bi. Given that =, =2 b where a…

A: These are complicated & lengthy problems,so I can do it in Advanced mathematics.

Q: Consider the complex number z = (1 – i)(-1-iv3). Find |2| and arg(2).

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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: 7) Convert the complex number, 3-5i, nto polar form, Show your work.

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Q: Divide the following complex numbers: (ComplexNumber)1 (ComplexNumber)2 1. (ComplexNumber)1: Real X1…

A: given that

Q: Rewrite the complex number 7e“ in a + bi form. Round to two decimal places.

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Q: 2+7i 3-3i

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Q: 2) Suppose 1 and w are complex numbers, show that Aw =

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Q: What is the result of multiplication of complex numbers -V3+i and (cos + i sin )? 3

A: Let z_1 = - sqrt 3 + i = r cos theta + i . r sin theta r cos theta = - sqrt 3 r sin theta = 1 Then…

Q: Use DeMoivre’s theorem to find (–8)1/3. Express your answer in complex form.

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Q: Express the given complex number in exponential form into a + bi form. 157 2e 6 1 + i3 - \3 + i 1 -…

A: The given complex number is ;                                     z = 2e5πi6 We have to find this…

Q: If X = 3 - j2     and    Y = 3 + j2   convert your pair of complex numbers to polar form

A: For X=3-j2:

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: Use DeMoivre’s theorem to find (–√3/2 +i/2)12. Express your answer in complex form.

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Q: iz = iz where z is a Complex number in a

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Q: Express the complex number z = 10 cis 315° in rectangular form a + bi.

A: Given the complex numberz=10cis315°

Q: Write down the definition of the complex conjugate, ž, of z = a + ib where a, b are real number…

A: Complex conjugate of a complex number z is defined as a complex number which has same real part as z…

Q: True or False The polar form of a nonzero complex number is unique.

A: The polar form of a nonzero complex number is unique.

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: if complex numbers Z1= 4.5-j5.1 , Z2= 3.2- j6.2, Z3= 2.25-j5.6 , Z4= 7.5-j9.2 , then calculate…

A: Given complex numbers are…

Q: What is the complex conjugate of 2 – 3i ?

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Q: Suppose z is a complex number that possesses a fourth root w that is neither real nor pure…

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Q: Write the complex number z = 2 - j2 in polar O 2.83245° O 2.832-315° O 2.832-45° O -2.832-45°

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Q: Find the sum of the complex numbers in the complex plane. Imaginary axis 10 8 (4, 7) 6 4 2 6 8 Real…

A: To find :               The sum of complex number in complex plane.         Adding/Subtracting…

Q: B. Express in the form of a complex number x+iy 1. (2+34)+(-4+5i) 2. (3+ 2i)(3 – 31) 8+4i 3. 1-i

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Q: Calculate these complex numbers and express your results in rectangular form: 60/45° (a) 7.5- j10…

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Q: 6 Convert your original pair of complex numbers to polar form. D = 1-j2

A: Since you have asked multiple questions in a single request we would be answering only the first…

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

A: 3+3i5 Consider, z=3+3i Now, z=32+32=32&θ=tan-1yx=tan-133=tan-11=π4 Now trigonometric form is,…

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: complex numbers.

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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: Express the complex number z = 6 cis 0° in rectangular form a + bi. Provide your answer below:

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Q: 6+5i -6-3i 2s

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Q: The variable z is often used to denote a complex number and 7 is used to denote its conjugate. If z…

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Q: If Z1, Z2 are complex number then |Z1 Z2|2|Z1 ||Z2| True False

A: Given ;Z1Z2≥Z1Z2

Q: a

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Q: Express as complex number a. (V(9) - v(-9))*( v(-36) b. V(-16) *(V(25) - V(-25) ) c. (3+ 2v(-9) ) *…

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Q: Show that if z1 and z2 are complex numbers then (z1/22) = Zī/22.

A: Given, z1 and z2 are two complex numbers and we have to show,

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

A: z=x+iyThen,z-i=2x+iy-i=2x+iy-1=2…

Q: Ifz is a complex number, then sin-z can be written as (A)-i In iz+ (1-z) (B)t In [iz + (1 -z)]…

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Q: Prove that x^2 = 4 will result into ± 2 using complex numbers.

A: Given that, x2=4

Q: what are the complex numbers z1 and z2? for z1 i got z1= 3(cospi/12 + isinpi/2), z2= 2(cos7pi/12 +…

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