Write the following numbers in the polar form re", 0 < 0 < 27: (a) 5 , 0 = r = (b) 8 + 8i r = (c) -8 + 8i ||

Q: Express in the form a + bi where a and b are real numbers.

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Q: Find the product z,z2 and the quotient 2. Express your answers in polar form. z1 = 3(cos(250°) + i…

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Q: Let z = 7 (cos (7π/9) + i sin (7π/9))  and w = 6 (cos (2π/3) + i sin (2π/3)).  If zw is expressed…

A: Introduction: A complex number has many different representations. These are the rectangular…

Q: b Please convert the rectangular coördinates (5 5) and (-2 -2/3) to polar cOörd

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Q: swer in polar form where r> 0 and

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Q: Put in polar form z -3(cos(6) + i sin(6)). What is its principle argument, Arg(z)?

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Q: Evaluate and write your answer in a + bi form. [3(cos 82° + i sin 82°)]³ = Round to two decimal…

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Q: B)Convert r = √2 cos (0-) to cartesian.

A: we need to convert polar coordinate into cartesian.

Q: Express in the form a + bi where a and b are real numbers.

A: we have z = 12cos4π3+ isin4π3    Now 4π3= π+π3 hence z = 12cosπ+π3+ isinπ+π3               =…

Q: B)Convert r = √2 cos(0-) to cartesian.

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Q: Write the following complex trigonometric form r(cos0+isin O) with 0 (exact) in [0°,360°): numbers…

A: To write the following complex numbers in the trigonometric form  rcos θ+i sinθ with θ exact in [0°,…

Q: Find the product of z1 & Z2, leave answer in trigonometric form: 235 (cos플 + isin) & z2 =: +i sin 3…

A: We know that for  z1 = r1 cos θ1 + i sin θ1  and  z2 = r2 cos θ2 + i sin θ2 z1·z2 = r1·r2 cosθ1+θ2 +…

Q: Express in the form a + bi where a and b are real numbers.

A: To express: The expression 3cos3π2+isin3π2 in the form of a+ib. Given: The expression is…

Q: Express in the form a + bi where a and b are real numbers.

A: To: Express in the form a + bi where a and b are real numbers 5(cosπ+i sinπ)

Q: 1. Simplify (cos(4L25°) – tanh (0.3 + j0.7) cosh (In (3 + j5)(3+j5)) and write your final answer in…

A: Given expression is coshcos4∠25°-tanh0.3+j0.7ln3+j53+j5

Q: Q2) Convert the polar function r = tan20 to cartesian. %3D

A: Let's find.

Q: Find 3 additional polar representations of the point using -2pi<theta<2pi (-3,(-5pi/6)

A: We are to find 3 additional polar representations of the point using-2π&lt;θ&lt;2π-3 , -5π6

Q: test for symmetry and graph polar equation

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Q: 19) Find the area of one leaf of the graph of the polar curve. (Give answer as reduced fraction) r =…

A: Please consider the handwritten solution.

Q: 3. Simplify the following, giving the results in polar form (1) 3(cos 143° + j sin 143°) X 4(cos 57°…

A: Cos(x)+isin(x)=e^(ix) Please see the explanation below

Q: Use De Moivre’s theorem to write (cos π/5 + i sin π/5)^5 in the form of a +bi

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Q: If z = r cos 0 + ir sin 0 then 1 / z has absolute value __ and angle __ . Its polar form is __ .…

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Q: (a) 0 = %3D (b) 6 + 6i 0 = r = (c) —3 — 3і r = 0 =

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Q: Given z1 = 4 cos I isin and z2 = 2 cos I isin find z1z2 and 3 3 write the product in polar form.

A: Given: z1=4cos 4π3+i sin4π3  z2=2cos π2+i sinπ2   To find z1z2

Q: Find the product z,z2 and the quotient 1. Express your answers in polar form. 21 = 7(co() + i sin ),…

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Q: Find the areas of the regions in the polar coordinate plane described Enclosed by one leaf of the…

A: Area of the region bounded by r=fθ between the radial line α to β is A=12∫αβr2dθ

Q: find the area of the polar curve.   r=3-sin@

A: To calculate the area of the given polar curve , using integration

Q: Write z1 and z2 in polar form. z1 =sqrt(3) + i , z2 = 1+sqrt(3)*i 1/z2 =

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Q: Express the following in polar form): (iii) (cos 300° + i sin 30"). 2 i) sin 60° + i cos 60° (ii)…

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Q: Given that z = 1- iv3, express z in the form r(cos 0 +i sin 0). Hence write down z' in the form…

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Q: Find the area of the region inside one leaf of the polar graph: r = sin7x

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Q: Q2) Convert the polar function r = tan20 to cartesian

A: We know that x = rcosθ, y=rsinθ Given: r=tan2θ

Q: Write the following with trigonometric form : 1) z = -V6 - V2i 2) z = -3i 3) z = 3 + 4i 4) z = -2 +…

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Q: Find the product z1z2 and the quotient 2. Express your answers in polar form. 22 Z1 = V5( + i sin ),…

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Q: Write the following numbers in the polar form re", 0 < 0 < 2T: 1 (a) 7 r = (b) 5 + 5i r = 0 = (c) 8…

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Q: Find the area of the region inside one leaf of the polar graph: r = sin4x

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Q: Convert the rectangular coordinates (4, 0) into polar form. Express the angle using radians in terms…

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Q: 1. What is the polar form of (5-jl5) × (8+j6)?

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Q: (b) Use De Moivre's theorem to find an expression for cos40 in terms of sin e only.

A: De Moivre's theorem gives the formula for calculating the powers of complex numbers. Formula of this…

Q: 6) Perform the indicated operations. Leave the resul in polar form. [50(cos 236° + j sin…

A: Given, 50cos236°+jsin236°2cos84°+jsin84°125cos47°+jsin47°

Q: 5. If x = 5cis(2.945)and y = cis( – 0.755) find xy³. Leave your answer in polar form. Note the…

A: If x=5 cis2.945 and y=cis-0.755, then to find xy3.

Q: find wz and z/w anwer in polar form z=3(cos130 degrees+i sin 130 degrees) w=4(cos270 degrees+i…

A: We have given z = 3(cos130° + i sin 130°) w = 4(cos270° +i sin270°)

Q: Find z,z2 in polar form. 21 = 2 (co여(플) +i sin(플)); 22 =4( cos +i

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Q: Find three additional polar representations of the point, using -2pi<Ø<2pi (3, 3pi/4)

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Q: Find z1z2 in polar form. = 4 (cos(140°)+i sin(140°)); z2 = (cos cos(40°)+i sin(40°) Z1

A: We use the fact that  Cost+ i Sint = eit

Q: Remember that rectangular form is z = a + bi and that polar form is z r(cos 0 + i sin 0) Take…

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

Q: Convert In(x) = 5 to an equation in polar coordinates of the form r = f(0). (Use symbolic notation…

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Q: Q2) Convert the polar function r tan20 to cartesian.

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Q: Find the product z1 z2, expressed in polar form, if: 2; = cos +isin 2 co0 + isin = cos 12 12

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Q: Convert the followig into polar form,  2y=x-x3-xy2

A: The relation between cartesian coordinates x, y and polar coordinates r, θ is given by: x=r cosθ;…