2. Write the following complex numbers in polar form. (a) 2', (b) e-. 3. Prove the = e-" where z and w are complex numbers. 4. Find all the roots of the equations below where z € C. (a) 2* = 1, (b) 522 + 2: + 10 = 0.

Q: Write the complex number z =(-1+3i) in polar form: z = T(cos 0+isin 0) where and 0 The angle should…

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Q: 1- Represent the following complex numbers in polar coordinate Z= 2 + 5j Y= -3 - 3j

A: Z=2+5j compare the complex number with z=a+bj a=2b=5 find the modulus r  r=a2+b2=22+52=4+25=29…

Q: Express the complex number z = 6 in polar form r cis 0.

A: given,          z=6

Q: Express the complex number z = 1 + v3i in polar form r cis 0. Select the correct answer below: O 2…

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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: 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: 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: Convert the given complex numbers to the required equivalent form: 1. 62 + j25 into polar form Ans.…

A: Kindly go through the solution and let me know in case of any doubt or further clarification in the…

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: Let z be a complex number with |z = 11 and let z0 = 17 – 20i. What is |z – z0| + |z+ zo|??

A: Given:- Let z be complex number with |z| =11 and z0 =17 -20i  To find:- value of |z - z0 |2 +  |z…

Q: Convert the complex number from the given polar form to the rectangular form x+ yj. 18(cos180° +jsin…

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

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Q: Let z be a complex number. Then i(cosh(3z) + sinh(3z)) a, ie3z b. ie-3z с. е 3г

A: The given expression is icosh3z+sinh3z where z is a complex number.

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: Express the complex number z = 10 cis 315° in rectangular form a + bi.

A: Given the complex numberz=10cis315°

Q: Given a complex number w =. TM UTM UT iv3) by giving your answers in i. Express w in polar UT4 ii.…

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

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Q: 8) Use DeMoivre's Theorem to compute the three cube roots of v3+j. Write your answers both in polar…

A: First, let us compare the given complex number to the standard form of z=x+j y as shown below. x=3…

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

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Q: (15) For the complex number z = ti find z2 by a) directly multiplying in the rectangular form given,…

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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: Express the complex number z=-4 in polar form r cis8.

A: z= -4 can be written as z= -4 + 0i  -4+0i is on the negative x axis.

Q: 2. Find the Cartesian (x+iy) form of this complex number 3π 3π Z=4(cos + 2 isin 377)

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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: The polar form of the complex number –3/3 + 3i is 6(cos(150°) + isen(150°)) 6(cos(300°) +…

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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: hich of the following is equivalent to (3 +3i/3)"? (Hint: You may want to convert the complex number…

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Q: Express the complex no v3 + i in polar form. Also show it by Argand diagram

A: Given that z=3+i convert the given complex number into polar form  also draw the Armand diagram

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

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

A: Root of complex number

Q: Express the complex number z = –1 – V3i in polar form r cis 0. Select the correct answer below:

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Q: Let z be a complex number. Then i(cosh(3z)+sinh(3z))=e^(3z)?

A: Explanation of the answer is as follows

Q: Q3 Put the complex number Z = 18 + 26i in the "polar" form Z = rele where r, 0 ER and both r and 0…

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Q: Let z be a complex number .then e^(3z+i) is bounded over the set of complex numbers?

A: Let z is a complex number. Let f(z) = e(3z+i)  Let us assume that f(z) is bounded. Hence f(z) is an…

Q: Put the following complex number V3 + 4 1 -- 4 into polar form.

A: We have to find the polar form

Q: z = r(cos 0+isin 0).

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Q: Find all 10 complex solutions in polar form to z^10-8z^5+64=0.   Help me fast so that I will give…

A: Given an equation, z10-8z5+64=0. To determine the 10 complex solutions of the given equation. Let…

Q: =(-1= v3i)³

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Q: let xn= vn (cosuat i, sinya) and an= Vzlcos 42+ i' sinqe) be two complex numbers in polar form.…

A: Answer (5) Let ,  z1 = r1 (cos y1 + i sin y1) and z2 = r2 (cos y2 + i sin y2) be two complex numbers…

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: complex

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Q: Write the complex number z=−7 −3i in polar form: z=r(cosθ+isinθ) where:   r= and θ=   The…

A: Consider the complex number, z =  - 7 - 3i To compare the given complex with standard form of…

Q: If a is a complex number such th equation az²+z+1=0 has one p

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