|74. Notice that (r cis 0)² = (r cis 0)(r cis 0) = ² cis(0 + 0) = 2 cis 20. State in your own words how we can square a complex number in trigonometric form. (In the next section, we will develop this idea more fully.)

Q: Find the product of the two complex numbers. 21 = 3 (cos 10 +i sin 10") and zg=-2(cos 35" +i sin…

A: Given: x1=3(cos 10°+i sin10°) and x2=-2(cos 35°+i sin 35°)

Q: Find the product of the complex numbers z1 = 4(cos 15° + i sin 15°) and z2 = 7(cos 25° + i sin 25°).…

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Q: For the complex numbers z=8(cos 70° + isin 70°) and w=5(cos 210° + isin 210°), find the following.…

A: We know, for multiplying two complex numbers in polar form, we just need to multiply the moduli and…

Q: tan(; 2 - 2j)

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Q: The notation a + bi is called ________ form for a complex number, and the notationr(cos u + i sin u)…

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Q: Add the following two complex numbers: (3 + 2i) + (5 – 31). What do you notice?

A: Given that (3+2i)+(5-3i)

Q: From the topic of Trigonometric of Complex Numbers. Convert to complex number, sec(e2j)

A: we know that cosθ= ejθ+e-jθ2and cosθ=1secθso secθ=   2 ejθ+e-jθ

Q: Write the trigonometric form of the complex number. (Round your angles to two decimal places. Let 0…

A: Given: z = 77-i^  Comparing the given complex number with z=x+i^y, we get,  x = 77 , y = - 1. The…

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: Find the quotient z1/z2 of the complex numbers z1 = cos 80° + i sin 80° andz2 = cos 200° + i sin…

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Q: Find two square roots for the complex number. Leave your answers in trigonometric form. 81 cis 0° 9…

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Q: In polar form the complex number z = 3/2 + 3v2i can be expressed as (cos 45 +i sin 45 ). Let w = z3…

A: The given complex number,   z=32+32 i

Q: How may the following complex numbers be obtained fromz = x + iy geometrically? Sketch. 1 / z

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Q: Find the quotient z1/z2 of the complex numbers z1 = 12(cos 3π/4 + i sin3π/4) and z2 = 4(cos π/4 + i…

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Q: Given that the complex numbers zı and z2 are such that z, = cos 10° + i sin 10° and z2 cos 15° + i…

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Q: In this question we use the complex numbers x = 1 + 2i, y = 3-i, 3π 3π √2(cos ³4+ isin ³7). Complete…

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Q: find the quotient z1/z2 of the complex numbers z1 = 10(cos 10° + i sin 10°) and z2 = 5(cos 5° + i…

A: The complex numbers z1 = 10(cos 10° + i sin 10°) and z2 = 5(cos 5° + i sin 5°). We need to find the…

Q: Find two square roots for the following complex number. Leave your answers in trigonometric form. 81…

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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: Find the quotient z1/z2 of the complex numbers z1 = 3(cos π/5 + i sin π/5)and z2 = 4(cos π/10 + i…

A: Given:         z1 = 3(cos π/5 + i sin π/5)  and        z2 =  4(cos π/10 + i sin π/10)

Q: 4. If the two complex numbers z1=ri(cos01+ i sin 01) and z2= r2(cos 02+ i sin 02) then the numbers…

A: The given complex numbers,z1=r1cosθ1+i sinθ1 and z2=r2cosθ2+i sinθ2

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

A: Here, z1=5i z2=6+4i

Q: The quotient of z1 =6 cis (2/3); z2 =2 cis (1/6) in trigonometric form is;

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Q: From the topic of Trigonometric of Complex Numbers. Convert to complex number, sin(4+7j)

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Q: 2 10 -2- -4 -6- -8- nd 3 – 2i, then find their product as a complex number. pllowing table: es…

A: We have to find the following conditions according to the given information

Q: find two square roots for the complex number 4 ( cos 50° + i sin 50° ) W0=? W1=? Then graph two…

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Q: Find two square roots for the following complex number. Leave your answers in trigonometric form. 64…

A: Solution

Q: Find the product of the complex numbers z1 = cos 210° + i sin 210° and z2 = cos 55° + i sin 55°.…

A: cosθ+i sin θ=ejθ

Q: Give the solutions of the complex equation –3z°(1 + i) = z(1 – i) in trigonometric for

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Q: Convert the complex number in standard from to cis form r cis 0 Write 0 in degrees between ) <0 <…

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Q: Give an example of a reduced cubic in the form x = 3px + 2q with three real roots but where q – p³ <…

A: Question: Give an example of a reduced cubic in the form x3=3px+2q with three real roots but where…

Q: Question 4 Solve the following complex roots and plot the solutions if (z – 5+i)° = -729. Question 5…

A: Q4)  z-5+i6=-729                      =-36                      =36-1…

Q: What is the result of multiplication of complex numbers -V3+i and 끓 (cos +isin )? A 을 (cos +i sin )…

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Q: From the topic of Trigonometric of Complex Numbers. Evaluate tan-1(1+j).

A: Given  To evaluate tan-11+j

Q: Given the complex numbers  z = 8 (cos(8π/15) + i sin(8π/15))  w = 1/2 (cos(17π/15) + i…

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Q: Write the standard form of the complex number. (Round numerical values to four decimal places.)…

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Q: A) 16 sin37 = %3D B) cos53 16

A: Given: To find the correct equation.

Q: From the following rectangular complex number Z-4+3i, Z-2-3i and Z,--5+2i Find the poler form?

A: Given:     z1=4+3i      z2=2-3i      z3=-5+2i For a complex number z, expressed in Cartesian form as…

Q: Find all the solutions of   18 sinz = 1.  note: z is a complex number, so please solve for the…

A: Please check step 2 for the solution.!

Q: Consider the following complex number. Z = 4(cos (280°) + i sin (280°)) (a) Find two square roots…

A: Root of complex number

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: Z, = 2 cis 30° Z2 = 3elli %3D Zz = In (1 + i)

A: Given: Z1=2cis30° Z2=3eπi Z3=ln1+i Z=Z1Z2+Z3 Z1=2cis30°     =2cos30°+isin30°      =232+i2…

Q: 2) Combine the following complex and imaginary numbers: a. (3+ 2i) + 2 + 3i b. (3 + 2i) (2 + 3i) 3)…

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Q: Express the complex number -2i in the form R(cos(0) + i sin (0)) = Re where R> 0 and 0 ≤ 0 ≤ 2T.…

A: Express the complex number

Q: Fihd the cube roots of the complex ber z = 125 (cos(210°) + i sin(210°)). Select all correct…

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Q: Find the quotient z1/z2 of the complex numbers z1 = 5(cos 4π/3 + i sin 4π/3)z2 = 10 (cos π/3 + i sin…

A: Given,   z1=5(cos4π3+i sin4π3)  andz2=10(cosπ3+i sinπ3) To find quotient z1z2: We know that,…

Q: Exer. 21–46: Express the complex number in trigonometric form with 0 so<27. 25 2V3 + 2i 4 cis 37 29…

A: Given: The complex number 25) 23+2i. 29) -20i 34) -5.