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

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

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

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: iree complex Z1 = 1- 2i, z2 = 6i, z2 = -3 -i. Compute the following, with your answer expressed in…

A: given that z1=1-2i,z2=6i,z3=-3-i find a)z1+z2z3b)3z2*-4z1z1c)z1z2*-3iz3

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: Express the product of 9i5(2i³ - 3i16) in a + bi form.

A: 9i15(2i3-3i16) =(9i15)(2i3)-(9i15)(3i16) =18i15+3 -27i(15+16) =18i18 - 27i31 Now i=√(-1) i18=-1…

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: 3. Evaluate the following complex number a. (30460° +20<-20°) b. 302-30° +(4-j3)(3+j4)(4-j5)* C.…

A:

Q: What is the argument of the complex number given by z = (1+ iv3)(1 + i)(cos(0) + isin(0)) Select…

A: We have to find argument.

Q: present given complex number in polar form also find its (1+21) ¹2 (-2-√5i)"

A:

Q: Simplify the complex number a = that a= a + bi. 10 (1+1) ". That is, find values for a, b = R such

A:

Q: Q1) Find modZ and ArgZ for the complex numbers given below: 1+i√2 1-i√2 2 2+i a) Z= b) Z= +2-i

A:

Q: Find the modulus and argument of the com

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

Q: Find the modulus and argument of the following complex number. z= (3+2j) (- 1+2j), giving the…

A:

Q: Find the modulus and argument of the following complex number. z=(3-2j) (1+2j), giving the principal…

A:

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

A:

Q: Determine Re(z) if z = 1145x-6512yi   Sucject: complex numbers

A: We have a complex number, z = 1145x - 6512yi We know that, In a complex number  z = a + bi  , a  is…

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: Find the product in the complex plane 1/4(cos Pi/6 +i sin pi/6) + 8 (cos pi/6 + i sin pi/6)

A:

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

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

A:

Q: bers are conjugate. If z, and z2 are two non-zero complex numbers st jal arg (2) ) - arg (z2 ).

A: Since we know that, | Z1 + Z2 | = |Z1| + |Z2| only when the the point Z1 , Z2 and origin are…

Q: 7. Express the complex number 1/(1+ jV3) in the form Aejº

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: them with v and w. (Hint: 3/3 = 5.2) | argument of v and w. Im Re 64-2 Re(v) = Im(v) = lv] = Arg(v)…

A:

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

A: given

Q: #2. If 2₁ and 2₂ are two complex numbers, show that 12₁-221² + 12₁ +221² = 2 ( 1211² + 122 1²).

A: 2. Let z1 = a + bi and z2 = c + di be two complex numbers.      Then,          |z1|2 = a2 + b2…

Q: For the following complex numbers z1 and zą, find z,z2 and 4 Write the number in the form a + ib. z1…

A: Polar form of a complex number Any non-zero complex number z=x+iy can be expressed as  z=rcos θ+i…

Q: a

A: