5) Given the complex number z = -3+ 3i, a) Write z in polar form. b) Find z2 in polar form.

Q: Find the quotient z1/z2 of the complex numbers z1 = 2 - 2i and z2 = 1 - i. Leave answers in polar…

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Q: To convert a complex number from rectangular form, z = a + bi, to polar form, z = r(cos e + i sin…

A: We fill the blank spaces as,

Q: Q3/ convert cartesian complex number 3-9i into polar form

A: The given complex number is:3-9i To convert into the polar form.

Q: Suppose Zi and Z, are two given complex numbers. Construct graphically a. 3Z1 – 2Z2 b. (1/2)Z, +…

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Q: Find the polar form for the complex number -2-3i.

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Q: Write the complex number z = 4-4/3i in trigonometric form (sometimes called polar form). Express the…

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Q: As in the previous question, suppose z is a complex number (a point in the plane) with angle 30…

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Q: In an Argand diagram, O is the origin and the points P and Q represent the complex numbers z1 and z2…

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

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

A: Given:     Z = 3ei(4π/3)

Q: Convert the complex number, z=3cis(1/2 ⋅π) from polar to rectangular form. Enter your answer as a+bi

A: givenz=3cis(π2)orz=3(cosπ2+isinπ2)

Q: Express the complex number 2 + 2√3 i in polar (trigonometric) form.

A:

Q: The polar form complex number (Z=12i )is

A: given  complex number Z=12i

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: Write the complex number z = 1 + I square root of 3 in polar form with the angle in degrees.

A: given,         z=1+3i

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: If the complex number z = x + iy satisfies the condition |3z - 6i| = 3, then z lies on a. Circle…

A: We know that z=x+iy and z = x2+y2 Then 3z-6i = 33(x+iy)-6i = 33x+3iy-6i = 33x+(3y-6)i =…

Q: To convert a complex number from rectangular form,z = a + bi, to polar form, z = r(cos θ + i sin…

A: The rectangular form of a complex number is z=a+ib the polar form is z=rcosθ+isinθ

Q: Convert the polar form of the complex number to rectangular form . -2(cos(플) + isin(쫄))

A: Rectangular form x+jy Polar form r∠Θ r= √(x2 +y2 )  Θ= tan-1 (y/x)

Q: 8(cos(30°) + sin(30°)i) , from polar to rectangular form. Convert the complex number, z = Enter your…

A: Convert from polar to rectangular

Q: I. Write 2 – 7i in polar coordinates on the complex plane.

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

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Q: 7. Rewrite the complex number 4 + 7i into polar re" form.

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Q: O Express the complex number in the polar form -34i 5-3i

A: Answer

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: A complex number z has |z| =5 and arg z = 132⁰. i) Plot z on an argand diagram. ii) Write z in…

A: .

Q: Find the product of the complex numbers z1 = 4(cos 50° + i sin 50°) and z2 =  7(cos 100° + i sin…

A: Given complex numbers - z1 = 4cos50°+isin50°                ..........................(1)z2 =…

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: 1) What are the equations (4 of them) that show the relationship between polar and rectangular…

A: We can solve as follows

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: The polar form of a Complex Number is. .

A:

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: Let z be a complex number. Then cot(5z – n) is equal to

A: Since solve the first question for you. If you want any specific question to be solved then please…

Q: Find the complex cube roots of 1+i, leave your answer in polar form with the argument in degrees.

A: Consider the complex number  To find - complex cube root of z

Q: Determine the three cubic roots of the complex number (−10 + j6)5 in both polar and Cartesian forms,…

A: given a complex number  say w=-10+6j5 now ,  -102+62=100+36                    =136…

Q: 2Q: Express the complex number z=- = -2/4 +7i in polar form and also represent it graphically. Hence…

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

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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 complex number -3+/4 in the polar form.

A: Complex number in polar form.

Q: Write the complex number z = 5-5/3i in trigonometric form (sometimes called polar for Express the…

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Q: Find all the roots in the complex plane using De Moivre's Formula in polar form and rectangular…

A: Given the complex number 18 in polar form and rectangular form.

Q: If you are given a complex number in polar form, how do you write it in rectangular form?

A: The complex number in the polar form is written as z=rcosθ+isinθ. Solve further as follows:…

Q: 1- V3 i 1+v-3

A: Given : Z = ( 1 - √3 i )/(1+√-3)

Q: Convert the complex number 8 cos +i sin to polar form. Give exact answers for r and 0 (no decimals).

A:

Q: Write the complex number in polar form. 4+4i 4/2 (cos +i sin) (Type an exact answer in the first…

A: Given that, 4+4i Calculate the complex number in polar form.

Q: QI\ A Express the complex number (-1+5j) in polar form?

A:

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

Q: Given the complex numbers z = V2 + v2i, find the polar form.

A: We have to write the polar form.