Write z = 4(cos 120° + isin 120°) in rectangular form, a + bi.

Q: Find the quotient of z, & z2, leave answer in trigonometric form: z1 = 2 – 3i & z2 =1– V3i

A: Here, the given complex numbers are: z1=2-3i & z2=1-3i

Q: Replace the polar equation with an equivalent Cartesian equation. r 2 + 2r 2 sin θ cos θ = 576

A: Given: r2+2r2sinθ.cosθ=576 Solution: By taking common r2 we can write above equation,…

Q: Write the equation in the general form of r=7/(1-cosθ) using rectangular coordinates.

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Q: assume that all the given angles are in simplest form, so that if A is in QIV you may assume that…

A: Given  where A is in quadrant II

Q: Find the direction cosines and angles of u = −4i + 3j + 5k and show that     cos2      + cos2…

A: Then we find the angles

Q: Write the equation with rectangular coordinates. 2 = 2 cos 20 %D

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Q: Find the direction cosines and angles of u = 7i + j − k and show that                 cos2    + cos2…

A: Direction ratio of u = 7i + j − k is (7,1,-1) So the direction cosine is:

Q: Find the polar form of 1 + sqrt(3i)

A: Find the Polar form of complex number  Given z = 1 + √3i

Q: Convert the rectangular equation to polar form. Assume a > 0. x2 + y2 - 2ax 0 Select one: -2 O a.…

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Q: Convert from rectangular to polar form. 5 - 5i 05/2 (cos 135° + i sin 135°) 05/2 (cos 315° + i sin…

A: The given number, 5-5i

Q: Rewrite the polar equation r = 4 sin(0) as a Cartesian equation.

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Q: assume that a is an angle in standard position whose terminal side contains the point (5,-5) sin a…

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Q: Convert the equation to a rectangular equation. 7. 4-2 cos 0 3D0

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Q: Find the component form of u + v given the lengths of u and v and the angles that u and v make with…

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Q: photo attached

A: Given the polar equation

Q: Perform the indicated operation. Reduce to Rectangular Form 1.1 [2 (cos 25 + i sin 25)] * [5(cos 75…

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Q: Identify the surfaces of the following equations by converting them into equations in the Cartesian…

A: The given surface in spherical co-ordinate system is ρ=sin Φ sin θ     .......(1)

Q: In calculus, it can be shown that eiθ = cos θ + i sin θ. Use this result to plot the complex number…

A: Given: Complex number eπi/4

Q: Perform the indicated operation and convert your final answer to polar form z = r(cos® + isin®)…

A: Given query is to convert the expression in Polar form.

Q: Write the following numbers in the polar form re", 0 <0 < 2T: 1 (a) 2 r= ,0 %3D (b) 4 + 4i r3= ,0 =…

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Q: Perform the indicated operation: 8 [ cos (231°) + i sin (231°)] * 13 [ cos (332°) + i sin (332°) ]…

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Q: 2 = sin 0 – sec 0

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Q: Derive the Law of Cosines from the Pythagorean Theorem.

A: Consider the following figure: BC=aAB=bAC=cCD=a-bcosθ

Q: 413-4i

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Q: Let 0 be a quadrant I angle with cos(0)

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Q: Perform the indicated operation: 5 [ cos (275°) + i sin (275°) ] * 13 [ cos (268°) + i sin (268°) ]…

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Q: Convert to rectangular form. 2 = 1/(9 + cos? ®)

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Q: Use as shown  to prove the Law of Cosines (which is a generalization of the Pythagorean theorem): c2…

A: To find the cosine law as follows: The above figure can also be represented by:

Q: Find [2(cos 30° + i sin 30°)]5. Write the answer in rectangular form.

A: Trigonometry:  We need to find the value of the following    [2(cos 30°+isin 30°)]5

Q: Find [2(cos 20° + i sin 20°)]6. Write the answer in rectangular form, a + bi.

A: 2cos20°+isin20°6

Q: Write the following numbers in the polar form re", 0< 0 < 2n: (a) (b) 4 + 4i (c) 3 – 3i = A

A: Given:  (a)The number 16 (b)The number 4+4i (c)The number 3-3i To find: The polar form reiθ,…

Q: Indicate the quadrants in which the terminal side of θ must lie in. A): If sin θ 0 and csc θ 0,…

A: Recall: All trigonometry-ratio are positive in 1st quadrant. Sine and cosine are positive in 2nd…

Q: Use the unit circle to find all values of u between 0 and 2p for which cos theta = - 1/2

A: Given:          cos u = -12 To find:               The values of u between 0 and 2π.

Q: Find the direction cosines and angles of u = 5i + 3j − k and show that               cos2    + cos2…

A: u=5i+3j-k u=52+32+-12=35 Now direction cosines are, cosα=535cosβ=335cosγ=-135 Direction angles are,…

Q: Write in Polar form: r(cosθ+isinθ). 8+10i r=    , θ=

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Q: Write in polar form: 2- (cos(225°) + i sin(225°)) 7. (cos(80°) + i sin(80°))

A: Polar coordinates are representation of coordinates or points in 2-D plane using the radius r, and…

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

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Q: Write in polar form r(cos(θ)+sin(θ)i for each given rectangular form a+bi   (√3-i)=

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Q: Express in true polar form, z = 5(cos 55° -j sin 55°)

A: We have to express in true polar form z=5cos55°-jsin55°.

Q: Perform the indicated operation: 5 [ cos (275°) +i sin (275°) ] * 13 [ cos (268°) + i sin (268°) ]…

A: Proceed as shown...

Q: Calculate /3 – 2i. Give your answer in a + bi form. In polar form, use the angle 0-< 0 < 2n.

A: Solution is in step 2

Q: Calculate sqrt(2-3i). Give your answer in a+bi form and in polar form using the angle O less than or…

A: we have to calculate sqrt(2-3i). we have to give our answer in a+bi form and in polar form using the…

Q: Perform the given polar form into rectangular form complex number. 10 1+jv3 1-jv3,

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Q: Convert r= 4+cos (2•) into rectangular coordinates

A: Consider the polar equation