Consider the following. Square roots of 5(cos 90° + i sin 90°) (a) Use the formula zk = V r cos- 0 +360°k 0 + 360°k to find the indicated roots of the complex number. (Enter your answers in +i sin. trigonometric form. Let 0s0< 360°.) ZO = Z1 = (b) Represent each of the roots graphically. Imaginary Imaginary axis axis 31 31 2 2 1 Real Real -3 2 -1 1 2 3 axis 3 axis -3 -2 -1 -2 -3

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: Find all the complex square roots of w = 9( cos 45° + i sin 45°). Write the roots in polar form with…

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Q: Find all the complex square roots of w 64(cos 30+ i sin 30"). Write the roots in polar form with 0…

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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: Given the two complex numbers: 2₁ = 2 + 4i and Z₂ = √5 -3i 1) Find the value of the complex number…

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Q: (a) Use the formula zk = Vr(co e+ 27tk cos +i sin 0+277K to find the indicated roots of the complex…

A: Given Z=-322(-1+i) Zk=rncosθ+2πkn+sinθ+2πkn, 0≤θ&lt;2π The trigonometric form of the complex number…

Q: Given the two complex numbers: z1 = 6(cos π/2 + i sin π/2) and z2= 3/2(cos π/4 + i sin π/4) Find the…

A: we have to find

Q: Given the complex number z1 12( cos +i sin ) and 13 %3D 8 8. z2 = 2( cos +i sin ), express the…

A: Given two complex numbers, z1=12cos13π8+ι sin13π8 and z2=2cos11π8+ι sin11π8 We have to express  z1z2…

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: Consider the following. Cube roots of -343 0 + 2xk 0 + 2rk (a) Use the formula z = V7(cos + i sin to…

A: The detailed solution is as follows below:

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: Consider the following. Square roots of 7(cos 120° + i sin 120°) 0 + 360°k cos 0 + 360°k to find the…

A: Topic‐ complex number

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

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Q: Express the complex number z = 4 – 4/3i in polar form r(cos 0 + i sin 0). Provide your answer below:…

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Q: Find the three unique cube roots wk of the complex number z = 8 (cos 48° + i sin 48°). Write exact…

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Q: Convert the complex number to trigonometric form: r (cos 0 + i sin 0). Round your answer to 3…

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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: Consider the following. Square roots of -36/ (a) Use the formula z • Vilcos! 0+2rk n Zo - Z₁ = (b)…

A: Solve the following

Q: Find the quotient z1/z2 of the complex numbers z1 = 50(cos 4π/3 + i sin 4π/3) and z2 = 5(cos π/3 + i…

A: Find the quotient z1/z2 of the complex numbers .

Q: 11 Convert the complex number 8( cos 11T + i sin to polar form. Give exact answers for r and 0 (no…

A: Given :- Polar form, 8(cos(11π/6) + i sin(11π/6))   where, θ = 11π/6 and r = 8   = 8(cos(11π/6) + i…

Q: Convert the given complex number from the given rectangular to the polar form of r(cos 0+j sin 0).…

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Q: 6. Find all complex cube roots of 27(cos 219° +i sin 219°).

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Q: Find all the complex fourth roots in rectangular form of w = 64 cos +i sin %3D (Type your answer in…

A: To find the fourth root of the given complex number.

Q: Express the complex number z = -6/3 – 6i in polar form r(cos 0+ i sin 0). Provide your answer below:…

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Q: zk =nsquare route r (cos theta +360 degreesk/n +i sin theta +360 degreesk/n)

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Q: For a positive integer n, the complex number z = r(cos e + i sin 0) has exactly n distinct nth roots…

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Q: Find all the complex square roots of w= 9( cos 45° + i sin 45°). Write the roots in polar form with…

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

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Q: Consider the following. Square roots of −49i (a) Use the formula zk = nth root r [cos ((θ + 2πk ) /…

A: Given a complex number -49i

Q: For a positive integer n, the complex number z = r(cos 0 + i sin 0) has exactly n distinct nth roots…

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Q: 3(cos i sin ) and Given the complex number z1 22 = 3( cos +i sin ), express the result of 21 22 in…

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Q: Find the quotient z1/z2 of the complex numbers z1 = cos 70° + i sin 70° andz2 = cos 230° + i sin…

A: The two complex numbers are given as , z1=cos70°+isin70° z2=cos230°+isin230° The value of z1z2 can…

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: Find all the complex square roots of w= 9( cos 45° + i sin 45°). Write the roots in polar form with…

A: Let's Solve,

Q: Find the quotient z1/z2 of the complex numbers z1 = 50(cos 80° + i sin 80°) and z2 = 4(cos 25° + i…

A: We have to find quotient z1z2 of the complex numbers: z1=50cos 80°+i sin 80° and z2=4cos 25°+i sin…

Q: Find the quotient z1/z2 of the complex numbers z1 = 3(cos 5π/18 + i sin 5π/ 18) and z2 = 10(cos π/16…

A: Given two complex numberz1 = 3cos5π18 + i sin5π18z2 = 10cosπ16 + i sinπ16

Q: Consider the following complex number. z = 36(cos (210°) + i sin (210°)) (a) Find two square roots…

A: Using De-Moivre's theorem we get

Q: find all complex values z satisfying the given equation cosh z = 2+3i

A: We know that - cosh x= (ex-e-x)/2 using it, the explanation is given below-

Q: Find the quotient z1/z2 of the complex numbers z1 = 20(cos 75° + i sin 75°)z2 = 4(cos 25° + i sin…

A: Given complex numbers,  z1 = 20(cos 75° + i sin 75°) z2 = 4(cos 25° + i sin 25°) To find z1/z2

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: Find all the complex cube roots of w = 8( cos 270° + i sin 270°). Write the roots in polar form with…

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Q: Find all the complex square roots of w= 81(cos 30° + i sin 30°). Write the roots in polar form with…

A: Solution:- Complex root of w=81cos 30°+i sin 30°   wn=rcos θ+i sin θ wk=xr cosθ+2πkn +i sin θ+2πkn…

Q: logz, (z3":) \0gz;

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Q: Consider the following. Square roots of 4(cos 90° + i sin 90°) 0 + 360°k (a) Use the formula z =…

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Q: Write the complex number z =1-2i in trigonometric form (sometimes called polar form). Express the…

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Q: Find all the complex square roots of w 9( cos 45° + i sin 45°). Write the roots in polar form with 0…

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Q: Find the four fourth roots of z= cos 4p/3 i+ sin 4p/3 . Leave your answers in trigonomet-ric form.

A: De Moivre's law: cosθ+isinθn=cos nθ+isin nθ.

Q: Write the complex number z= 6+3i in trigonometric form (sometimes called polar form). Express the…

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Q: Given the complex numbers z1 = 5 (cos(139°) + i sin(139°)) and z2 = 2 (cos(-94°) + i sin(-94°)),…

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