a) 2+2v3i b) -5+ V3i c) =V6– v2i VZi d) –3i

Q: Write the complex number 4 COS 7π 4 7π + i sin 4 in the form a + bi.

A: Complex numbers is given in form of a+bi.

Q: Graph the complex number, find its modulus and put the complex number n in polar form with arguement…

A: Given complex number z = -5 + 5√3i.Graph the complex number.

Q: Convert the complex number from polar form to rectangular form, a+bi. 5n 14.7 cos 5n +i sin 6 The…

A: The polar form of the complex number is given as 14.7cos 5π6+i sin 5π6 The polar form of the complex…

Q: Consider the complex numbers: z = 2 – i and w = 1+3i . Sketch (in the same diagram) 2, w, zw and z:

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Q: If Z=a+2i is a complex number, the fundamental value of its amplitude 5TT/6.find the value of a and…

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Q: Use DeMoivre's Theorem to find the indicated power of the complex number. Write the answer in…

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Q: 11.Write the complex number 3e in polar and rectangular form

A: Given:     Z = 3ei(4π/3)

Q: Let z be a complex number. Then cot(5z-pi) = cot(5z)?

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Q: Write the complex number z =-2/3 -2i in trigonometric form (sometimes called polar form). Express…

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Q: Write the complex number z=-2+2i in trigonometric form (sometimes called polar form). Express the…

A: Solve the following

Q: 1- Represent the following complex numbers in polar coordinate Z= 2 + 5j Y= -3 3j D= -2 + 6j 2- Find…

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Q: Evaluate the given complex number. z=[tan(1-i)]^[cot(1+i)]

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Q: Find the midpoint of the line segment joining the points corresponding to the complex numbers in the…

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Q: Find the midpoint of the line segment joining the points corresponding to the complex numbers in the…

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Q: Graph the complex number, find its modulus and put the complex number in polar form with arguement Θ…

A: -1 - sqrt(3)/3 i = -1 - 0.577i (approx) This is similar as (-1,-0.577). Plotted it on graph.

Q: Find the product of the complex numbers z1 = 1 + i and z2 = -1 + i. Leave answers in polar form.

A: z1=1+i  &  z2=-1+i

Q: The complex number (−9+7i)/(9+5i) rewritten in Cartesian form is?

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Q: 12. Write the complex number -4 + 4i in polar and exponer

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Q: The complex number (cos+ i sin can be expressed in the form a + bi, where a, be R, as 31. COS 27 27…

A: solution:-

Q: What is the product (4/3 – 4i)( /2 + V2i) in polar form? In what quadrant of the complex plane does…

A: First multiply both the factors and then find magnitude and the angle to convert it in the polar…

Q: 5+ V4 i = Z 5-6i

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Q: The magnitude of the complex number esin(teta)+jcos(teta) is

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Q: b) Given the complex number z = -V32 + V32i. i. Express z in polar form. Vz and sketch ii. Obtain…

A: ----------------------------------------------------- Given: z = -32 + 32iAim: To express 'z' in…

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: The ________ ________ of the complex number a + bi is the distance between the origin and (a, b)

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Q: B. Find the indicated powers of the given complex number. Express the result in polar form, then…

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Q: (3+ /3i) (-1-i)?

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Q: Take the last four digits ABCD of your student identification number, and let z1 = A + Bi and z2 = C…

A: We will be taking the last 4 digits as ABCD. Let z1 = A + Bi and z2 = C + Di be the corresponding…

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: Graph the complex number, find its modulus and put the complex number in polar form with arguement Θ…

A: Graph the given complex numbers as shown below.

Q: (a) Make use of De Moivre's Theorem to calculate (3√3+3i)5 and leave your answer in the form a + ib.…

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the quotient z1/z2 of the complex numbers.Leave answers in polar form.Express the argument as…

A: Given, z1=2+2iz2=1+i

Q: By plotting the points on a scratch piece of graph paper, determine which complex number has the…

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Q: 1. the complex numbers given in polar form (re®) explain a) 2+2v3i b) -5 + V3i c) -V6 – VZi d) -3i

A: See the attachment

Q: Find the product of the given complex numbers in polar form. 3 (cos +i sin 푸).4 (cos (-표) + isin…

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Q: Find the product of the complex numbers z1 = 1 + i and z2 = 2 + 2i. Leave answers in polar form.

A: First multiply the given complex numbers. z1·z2=1+i2+2i=2+2i+2i-2=4i Obtain r. r=42r=4

Q: Given the polar coordinates of a complex number as (5,(−3/4)π), the corresponding Cartesian form is?

A: See the attachment

Q: Let z, and z, be the complex numbers given in the following argand diagram. Find the complex number…

A: First I am going to find the complex number by using the Euler's identity and then solve the problem…

Q: Find the indicated powers of the given complex number. Express the result in polar form, then…

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Q: On an Argand diagram the points A, B and C represent the complex numbers a, ß and y respectively.…

A: ARGAND DIAGRAM The point represented by a+z-aeiθ is a rotation by θ anticlockwise about the point…

Q: Use de Moivre’s formula to find the Cartesian form of the complex number  (-2 + 2√3i)7

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Q: Given the complex numbers z1 = 20 (cos(52°) + i sin(52°)) and z2 = 5 (cos(39°)+i sin(39°)), find the…

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Q: Write the complex number in trigonometric form. 3j 3j =(cos+jsin) (Use angle measures greater than…

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Q: Find the midpoint of the line segment joining the points corresponding to the complex numbers in the…

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Q: Express the given complex number in rectangular form. Express components in exact form. (No decimal…

A: Given query is to find rectangular form.

Q: Write the complex number in polar form with argument e between 0 and 2N. 6 + 6V3i

A: We have to find the polar form

Q: In the polar form of a complex number,r(cos θ + i sin θ), r is called the__________ and θ is called…

A: Given:Polar form of complex numberrcosθ +i sinθ