7. Write the following complex numbers in standart form a + bi e2+3ir log(-1+ iv3), the principal value of i", the principal value of (1 – i)*i

Q: 12. Use Euler's formula to write each of the following complex numbers in the form a + bi. (a) emi/3…

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Q: 4. Find the modulus, Iz], and argument, 0 , of the complex number. -1 + i

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Q: 5) Compute the fllowing complex numbers in standard arbi form for a, bE R. List all values if there…

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Q: write the standard form of the complex number 7/4(cos(3pi/4)+isin(3pi/4))

A: Here cos3π4=cosπ-π4                =-cosπ4                =-12 sin3π4=sinπ-π4               =sinπ4…

Q: express  in the form z = x +yi the complex number z whose modulus and argument are given.  |z| =…

A: z= x+iyz=12,    arg(2) =-π3modulus of z =z = x2+y2 =12⇒x2+y2 =12     -(i)

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: Solve the following  complex numbers in their rectangular form

A: Given,             Z3Z2 Where in Z2 = 5e2i and Z3 = 4 cos 40°

Q: 3. Convert the Complex number 10V3- 10i to trigonometric form: r(cos(0) + i sin(0)). 4. Let z =…

A: I have Provided this answer in step-2.

Q: Express the following complex number in the form x + iy respectively 3em/2

A: The given complex number is 3eiπ2. Write the given complex number in the standard form.…

Q: 3i

A: First we have to write in the polar form basis, z=r(cosθ+isinθ) Given : z=(4-5i)cos(1+3i) To…

Q: ii) How would you describe geometrically the relationship between a nonzero complex number z = a +…

A: Given: Describe geometrically the relationship between z=a+ib anda. −zb. z−1

Q: Express in the form a + bi where a and b are real numbers.

A: we have z = 12cos4π3+ isin4π3    Now 4π3= π+π3 hence z = 12cosπ+π3+ isinπ+π3               =…

Q: In(2) The complex number e is equivalent to a) ji b) (1+j} c) 1+ j d) 1- j

A: According to the problem, we have

Q: 6. Determine the order of the following complex number! о( со COS 3 57 3 +i· sin 3 -

A: That's easy. Have a great day!!!

Q: Let z be a complex number. Then cos(3z)-i is unbounded in C.* True False

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Q: 2. Write the number (2 – i)(-1+3i)(3 – 4i) in the form of +bi .

A: The detailed solution is as follows below:

Q: 2019 in + 3 E1028 2n +31028

A: As per honor code, we are entitled to solve only 1 question at a time so I am providing you the…

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: Find the four fourth roots of z = 625( cos 47 + i in ). Write each root in standard form. Wo = W1 =…

A: This question can be solved using the concept of fourth root of complex numbers.

Q: Write the complex number z = 18 + 18j in trigonometric form O 19.7(cos23.96°+ j sin 23.96°) O…

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

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Q: 5. [10] Use DeMoivre's Theorem to expand [4(cos 60° +i sin 60°)]". Write your answer in a + bi form.…

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Q: Express the following complex numbers in the form a + bi, a. 5(cos 0° + i sin 0º) b. 2(cos 30° + i…

A: A complex number is of the form a+ib  where,   real part is a and,  b is imaginary part of the…

Q: Find the modulus (r) for the given complex number z = -6.3 + 8.2i.

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Q: Solve the following  complex numbers in their rectangular form.  Where in Z1=2+4i, Z2 = 5e2i and Z3…

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

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Q: Express the following complex number in exponential form: (3 - 4) O -V5e-5.36/ 5e5.361 5e-5.36i…

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Q: Write the complex number z=(1-√3i)2015/(√2cis(7π/6))4028 in an exponential form.

A: cis(x) = cos(x)+isin(x)

Q: z=x+i y geometricaly ?

A: Given: a) z¯ b) -z c) 1z To find: The complex number obtained from geometrically.

Q: Find the four fourth roots of z = 81 ( cos 4pi/3 + isin 4pi/3 ). write each root in standard form

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Q: Let z be a complex number. Then the solution(s) of sinhz+coshz-e is (are)* None of these z=nti+1…

A: See solution below

Q: Let z1 = 4(cos 80° + i sin 80°) and z2 = 6(cos 145° + i sin 145°). Find the product z1z2 and write…

A: cos80° = 0.17sin80° = 0.98cos145° = -0.82sin145° = 0.57

Q: Find the imaginary component if the nth root of  a + bi is determined for a = 9, b = 3, and n = 6.…

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Q: Express the following complex number in exponential form: (-1 – 5) 3.1 e2.5i 5.1 e4.5i -5.1 e4.5i…

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

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Q: 17. The argument of the complex number z. where com CO is 1- i 13

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Q: Let z be a complex number satisfying 12|z|² = 2|z + 2|² + |z² + 1|² + 31. What is the value of z +-?…

A: Given that Let z be a complex number satisfying  12z2=2z+22+z2+12+31 To find the value of z+6z

Q: Let z be a complex number. Then cos(72)+3i is unbounded in C. False True

A: this is true , because

Q: Use Bombelli's approach to find a complex number c = a + bi such that = 18 + 26i where a and b are…

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Q: Find the three cube roots r1, r2 and r3 of 8(cos 264° + j sin 264°). Express all arguments in…

A: We have to find out cube root of unity for given complex number.

Q: Let z be a complex number. Then the solution(s) of sinhz+coshz=e is (are) * does not exist z=nti+1…

A: Given that z is a complex number. we have to find such z so that                              sinh…

Q: Find the imaginary component if the nth root of a + bi is determined for a = 10, b = 8, and n = 7.…

A: Imaginary component of the function

Q: Let z be a complex number. Then cos(72)+3i is unbounded in C.

A: A complex no. in the form of a+ ib

Q: Show that w = 2(cos 15° + i sin 15°) is a fourth root of z = 8 + 8iy3 by raising w to the fourth…

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Q: Let z be a complex number. Then the solution(s) of sinhz+coshz=e is (are) * O z=1 None of these does…

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Q: 1. Evaluate the principal value of the complex number : (3 + j4)(3+j4) O A. 3 + jo.592 О в.3-ј0.592…

A: Given: The complex number, 3+j43+j4   To evaluate: The principal value of the given complex number

Q: z = sin(e³) + sinh(5230°)

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Q: 4 9) Use Euler's formula to compute (--i. Express as a 2 2 complex number of the form a + bi.

A: