If Z is complex number e? = e*(cos y + isin y) True O False

Q: If Z = cos +i sin then Z²-Z+1=... O -2 O -2i O 2

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Q: If sinr = In y, show that dyOUTM dr OUTMO (1--- (1– 2) dy = y. dr

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Q: OR = {(r, 0): 0 <r< 6 cos(30), 0 < 0 < n}

A: Follow the procedure given below.

Q: Find the cartesian equation of the following: 6 1. r = 3-sin 0 2. r2 cos(20) = 4 %3D 9. 3. 4 sin(20)…

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Q: Prove that: Z, Z2 =r,r2[cos(8, + 02) + i sin(0, + 02)] 2=cos(0, - 62) + i sin(0, – 02)] Z2 3. (cos 0…

A: To prove given statement we need to first convert the polar co ordinate to Euler form then use…

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: Prove that: 1. Z, Z2 =r¡r2[cos(0, + 02) + i sin(0, + 02)]

A: According to our company policy we can only answer first question and rest of questions can be…

Q: 10. Derive the formula for the cos(z), where z is a complex number.

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Q: Question 9: Given that z = cos+ i sin and u- iv = (1+z)(1 − j²z²). Show that 30 2 V = utan r = 4²…

A: For any queries please let me know through comments. I will try to reply ASAP! Please like if…

Q: 2ーてスース+スニ。 A ind yh ans: スi:z )スてニリ人3:)

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Q: Find the product z₁z₂ and the quotient Z1Z2 = N 11 Express your answers in polar form. Z2 Z₁ =…

A: Given that, z1=10cos110°+isin110° and z2=2cos20°+isin20° Find the product z1z2 and the quotient z1z2…

Q: * DeMoivre's Theorem 4 (4(os 30 + ) i sin 30

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Q: Compute the Jacobian of : O(r, 0) = (9r cos 0, 4r sin 0)

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Q: snip

A: Given, cosjx,coskx, ∋j≠k, k≥1 if inner product of two function f(x), g(x) on the interval [a,b]…

Q: 4. Express the following in cartesian form. 2 2 cos 03 sin

A: Given r=22cosθ-3sinθTo express in cartesian form:

Q: by using the triangle method, Show that cos (21an n+1 %3D n2+1 n-1

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Q: 2п 2п 3. Find the fourth roots of 16 [cos(3 Hisin(). 3

A: Solution:-

Q: Let 2=x+iy be a complex number such that coshz#0. Then Re(tanhz) is equal to * sinhycoshy…

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

A: we need to convert polar coordinate into cartesian.

Q: 10/2 Use polar coordinates to evaluate dydx. O 5 O 1 O 4 O 2 O 6 03

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Q: z is a complex variable, z=x+iy question attached as photo

A: To verify the values of the two  given definite integrals

Q: Prove that: 1. Z, Z2 =r,r2[cos(8, + 02) + i sin(8, + 02)] 2.4=(cos(0, -62) + i sin(0, – 0,)] %3D 3.…

A: Here we use exponential form to represent complex Numbers.

Q: IF Z= Cos o+isin@ prove i tan %3D 2. 1ナて

A: we use Trigonometry identities to solve this Question

Q: Let z=x+iy be a complex number such that coshz#0. Then Im(tanhz) is equal to sinxcosx sinhycoshy…

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Q: Let , = cos-+i sin and z, = cos-+isin 6 Express in the form : =a+bi

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Q: Reduce to the form a + bi: a. sin (2 – i); b. cosh (1+ i).

A: Given: sin2-i cosh1+i To do: Reduce the given into the form a+bi.

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: Find the product of z1 = 2 (cos 213° + i sin 213 °) and Z2 = 4 (cos 33 ° + i sin 33 °) %3D

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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: Find the fourth roots of z= 16(cos 60 + i sin 60)

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Q: 1. The formula sinusinv 5(cos (u - v) - cos (u + v)] converts a product of sines to a of

A: sinusinv=12cosu-v-cosu+v

Q: Reduce to the form a + bi: a. sin (2 – i); b. cosh (1 + i).

A: Solution:-

Q: Let z=x+iy be a complex number such that coshz#0. Then Re(tanhz) is equal to * sinhxcoshx…

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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: verify the set {∅n = cos(nx) (∞ n=0) is orthogonal on the interval [−pi, pi]

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Q: ,2 - 1 If z = cis 0, show that i tan 0. 22 +1

A: this is complex analysis question and also very lengthy questions so I can do it in advanced…

Q: cos z = cos x cosh y– jsin x sinh y

A: Complex numbers

Q: 125 cos – j sin 11 7T 11 1. Simplify . Express answer in rectangular form. 47 + jsin 11 J5 cos 11

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

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 points of intersection of r = 1 andr = 1+2 cos 0.

A: General solution of cosθ = cosα is                           θ = 2nπ ±α

Q: ) Let Z= re q iy be a complex mumber Such that cosh Z+o. then Re (tanh z) is equal to Sin a cesn

A: In the given question we have to find the real part of tanhz and and also check it that is it equal…

Q: If the integration by parts was used to integrate the product of e^ax and sin(bx) and cos(bx).…

A: 1. To evaluate the integral ∫eaxcosbxdx+i∫eaxsinbxdx:

Q: Integrate the right side. cos u du + C 187

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Q: If Z +i sin( then Z-Z+1=... cos %3D 2 b 2- -2

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Q: Let z=x+iy be a complex number such that coshz+0. Then Re(tanhz) is equal to " sinhxcoshx…

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Q: Express 6(cos 2pi/3 + i sin 2pi/3) in the form of a +bi

A: Here the given polar form of a complex number is 6(cos2π3+isin2π3) . Now we express the polar form…

Q: Prove that: Z,Z2 =r,r2[cos(0, + 02) + i sin(0, + 02)] 1.

A: NOTE- As we are allowed to answer one question in one session so, i have answered first one for you.…