Miscellaneous Operation on Complex Numbers 1.-22+1 2.(2 + i) 3.cos h(i)

Q: be a let z:x+iy dos(3#0 Then Re (ten(37))is eq a Complex number suc

A: We have to find the real part of tan (3z).

Q: Justify these correct answers. (ALL) * Two complex numbers are given below. • x = –3+ 5i • y = 2 –…

A: Here  x = -3+5 i           y = 2-8 iNow x+y= (-3+5 i) + (2-8i)                  = (-3+2)+(5 i-8i)…

Q: 3+2 сos @ de 5+ 4 cos 0

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Q: Let z be a complex number. Then the solution(s) of sinhz+coshz=1/e is (are) O z=2nti-1 where n is an…

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Q: use the picture to find at least one complex number c such that z^7 + 3z^4 + c has exactly 3 zeroes…

A: consider the equation

Q: 4. X 211 3 12

A: multiplication

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

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Q: Find the Modulus of the following complex numbers: (a) 3 (b) (i + 1)(2 – i) (c) 2 – 3i

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Q: Expected answer: 718 + 11991 718 + 1199i (iii) (-2-j)º x Input the anwer in a + bi form, with…

A: De Moivre's Theorem z = r( cosθ + isinθ )then zn = rn( cosnθ + isinnθ ) where r is the modulus θ is…

Q: 1+i where i = -1, is Q.80 The argument of the complex number 1-i' (а) -п (b) 2 (c) 2 (d) 3 Ans. (c)

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Q: values of x and y. 9 + (x + y)i = 9 - i x + 2i = 9 + 2i ور

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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 ≤ 2. NOTE:…

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Q: 2Q Express the complex number 1+ 3i in the form x + yi, where x and y are real numbers. 1-2i

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Q: Justify your answer. Say if its true or false 1.- If z1, z2 and z3 are complex numbers such that…

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Q: a) Simplify the following expressions in standard form. (i) (5i"+6i° +2i?–3i*)+(-4+7i) 7-4i (ii) 2–…

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Q: 1- x-2 Before simplifying I wrote the complex fraction 1 - 5x-3' without negative exponents as 1 1 1…

A: Given1-x-21-5x-3=1-1x21-15x3=x2-1x25x3-15x3=x2-15x3-1·5x3x2=xx2-15x3-1

Q: 5. Graph the function and find the domain and range. 10 1 x + 6 x < -6 x +4 -6<x < 2 f(x) = 4 5 --x…

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Q: Add or subtract the complex numbers

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Q: Comolex unmber analysis Solve the following complex numbers 1.)  sinh[ln(8 + j0)] + cosh(8ej0.785)

A: We have to solve the given complex number sinhln8+0j+cosh8ej0.785

Q: 1. If z = 1+ iy is a complex number. Use the exponential form to compute (1+ /3 i)201

A: Definition used -            DeMoivre's theorem -             For a complex number z=r(cosθ+isinθ)…

Q: 2. Complex Operations Write the following complex numbers in the form a + bi. (b) (2+ 3i)(1 + i) 2+i…

A: Given: 2+3i4-i, 2+3i1+i, 11+i for converting given expression in a+bi  form, we apply given…

Q: 100 If G) = a + bi, compute for a and b.

A: To calculate the value of the complex fraction first simplify the fractions. The complex fractions…

Q: Let K = 6- 2i and E = 5 + 4i are complex numbers then find: (а) К — Е (b) E + K (с) К -Е (d) К/E

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Q: . Ifa complex number z has modulus 2 and argument , then

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Q: the complex number 6√3+6i in polar form 12(cos(n/6)+isin(n/6) 12(cos(n/4)+isin(n/4)…

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Q: 6. (a) Show that for all complex numbers z and w |z - w? + |z + w? = 2|2[² + 2|w/*. %3D (b) Let u, v…

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Q: -2 3. (a) Given complex numbers 2₁ = 1-i, 22 = 2 + 3i calculate 2₁² +22. in an (b) Illustrate the…

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