Q1/ Answer two only from the following: 1. Find the Multiplication Product of: -3m (Z, = 1+ v3 i) By (Z, = 3v2 cos+i sin") -3n 4 4 2. Determine the modulus and the principle argument for the complex number: (1+ i)? Z = 1- i

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Q: 2 1 Cof (A) i A = (5 -2 9 -6 5 US I -1 3.

A: The given matrxi is:A=32153-29-65To find its cofactor

Q: #4. Show that equation | 2-1-2|=1 Can be written as 121²2 Re Z-2 Im Z +1=0.

A: Given equation  z-1-i  =1. Show that: z2 -2 Rez -2 Imz +1=0.

Q: 4. (choose one.) (a) Find all 3rd roots of –8i. (b) Find all complex roots of the equation 26 = –9

A: 4) a) Given:          cube roots of -8i we write in trigonometric form:          =8cos-π2+isin-π2 we…

Q: 10 2) z = (-j)()

A: We have to use De Moivre's theorem cosθ+jsinθn=cosnθ+jsinnθ and Eular form of complex number…

Q: 1. (a) Find the four fourth roots of z =1+i. (b) Find the cube roots of z = i. 2. Find the…

A: NOTE: Due to multiple question answer for 1 and 2 is given here, for 3 and 4 ask in a new question.

Q: Show that T (1-i) cos- +isin- 40 40 (81-8√3) 6 10 = -√2

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Q: (i) Evaluate the complex number (a+bi)4n+2 + (b − ai) 4n+2 where n is any positive integer. (ii)…

A: This is a problem of complex analysis.

Q: bläi 4 * find each of a,& b 3 - i 2 – 2i - If a + ib = 2+ 3i then 1– 5i' -

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Q: Show that the equation cosx + x²³²-3 has a real root

A: Given: Equation: cos x+x3-3=e-xTo show: Given equation has a real root.

Q: Pleasantly, when we multiply a complex number z = a + bi by its complex conjugate z, we get a real…

A: 1+4i5-3i=1+4i5-3i*5+3i5+3i1+4i5-3i=(1+4i)(5+3i)52-(3i)21+4i5-3i=(5+3i+20i+12i2)25-9i21+4i5-3i=5+3i+2…

Q: #7. Find the four roots of the equation Z² +4=0 and use them to factor 24+4 into quadratic factors…

A: Answer:-

Q: Find all (real or complex) numbers z₁ and z2 such that 21+22=-6-3i Z1²2=3+11i

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Q: Find the modulus and argument of the com

A: Given,          7-xi5+3i2 and  x = 2.

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A: Consider the given identity

Q: 4 Get all the roots of 2(V3i – 1) |

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Q: #6. Find the square roots of (a) 2i; (b) 1-√3 i and express them in rectangular wordinates. #7. Find…

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Q: 1. Solve the following equations. a) (7+2/)+(4-3) b) (5-2/ (2-)(4+2) d) 2- 1+2 e) 21-3 2. Find x in…

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Q: 4. What is the simplification of the following complex expression (i? = -1) 5-i 3+i

A: To simplify the given complex expression:- 5-i3-i

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A: Given question says "Is it true that the quotient of two complex number is obtained by dividing…

Q: 2+J3 7-18 a) + 1-16 -5+/11 b) (5210°) (102-40°) (42-80°) (-6250°)

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Q: #1. Reduce each of these quantities to a real number 5i (1-2) (2-2) (3-2) (a) 1+2i 3-4i + 2-2 5 i…

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Q: +jsin- 12 12 + jsin 2. Simplify 3 cos .Express answer in rectangular form.

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Q: Verify that (¹)² = i²i but that (i²)i ‡ į²i ("i" imaginary unit)

A: What is Complex Number: A real number and an imaginary number are effectively combined to create a…

Q: 3) Find all the roots of the following equations z = √1-i 14 b) c) Z - i z = z = 964

A: a)

Q: ss Z3 to trigonometric form when z1 = 5+3i, z2 = 3+2i and z3 =

A: We have to express z3 as trigonometric form.

Q: 40 + 70j + j100 tan 0.67 = 100 100 + j(40 + 70j) tan 0.67 40–237.8j 40 + 70j + j100 × (-3.078) = 100…

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Q: rewrite the following complex numbers in z = x+ jy format

A: Since you have posted multipart question and we can answer three subparts. So, answered first three…

Q: Express each one of the following in the standard form a + ib. 1 (1+ i)? (iii) 3 - i (3+4i 1 + 1- 2i…

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Q: Q4-Find the complex roots of (4 + 4i)ō * (4 + 4i) (Demoivere's formula)

A: given

Q: The distance from the origin to the point that corresponds to a complex number is known as the…

A: The absolute value ( modulus ) gives the distance from the origin to that point z , where z…