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The Equation Z Bar Z A Bar Z Bar A Z Plus B Equal 0 B Belongs To R Represents A Circle If

Solution: |z+a|2 = |a2-b|, represents a circe if |a2|>b. Hence option (2) is the answer.... View Article

Length Of The Line Segment Joining The Points 1 I And 2 Plus 3i Is

Solution: Given points are –1 –i and 2 + 3i . Let A be (-1,-1) and B( be (2,3) Distance between AB = √((2+1)2+(3+1)2) (distance formula) =... View Article

If Z1 And Z2 Be The Nth Roots Of Unity Which Subtend Right Angle At The Origin Then N Must Be Of The Form

Solution: Given z1 and z2 be the nth roots of unity which subtend right angle at the origin. arg (z1/z2) = π/2 So z1/z2 = cos π/2 + i sin... View Article

If Argz Less Than 0 Then Arg Z Arg Z Equal

Solution: Let z = r (cos θ+i sin θ) arg (z) = θ < 0 -z = -r(cos θ+i sin θ) = r(cos (π+θ) +i sin (π+θ)) arg (-z) = π+θ arg (-z)-arg (z) =... View Article

The Value Of A B Omega C Omega B C Omega A Omega A B Omega C Omega C A Omega B Omega Will Be

Solution: (a+bω+cω2)/(b+cω+aω2) + (a+bω+cω2)/(c+aω+bω2) = [(a+bω+cω2)/(b+cω+aω2)]+(a+bω+cω2)ω/(c+aω+bω2)ω = [(a+bω+cω2)(1+ω)]/(b+cω+aω2)... View Article

The Value Of Cos 30 Plus I Sin 30 By Cos 60 I Sin 60 Is

Solution: (cos 300+i sin 300)/(cos 600-i sin 600) = [(√3/2)+i (½) ]/[(1/2)-(√3/2)i] = (√3+i)/(1-i√3) Multiply numerator and denominator with... View Article

If Z 25 By Z 1 5 Then Find The Value Of Z

Solution: Let z = x+iy |z| = √(x2+y2) …(i) Given |(z-25)/(z-1)| = 5 |(z-25)| = 5|(z-1)| |(x+iy-25)| = 5|(x+iy-1)| Squaring both sides,... View Article

The Radius Of The Circle Is Z I By Z Plus I Equal 5 Is Given By

Solution: |(z-i)/(z+i)| = 5 |(z-i)| = 5|(z+i)| Take z = x+iy |(x+(y-1)i| = 5|(x+(y+1)i| x2+(y-1)2 = 25(x2+(y+1)2) x2+y2-2y+1 =... View Article

If Omega Z And Omega Equal 1 Then Z Lies On

Solution: ω = z/(z-(⅓)i) |ω| = 1 |ω| = |z/(z-(⅓)i)| |z| = |(z-(⅓)i)| Put z = x+iy |3x+i(3y-1)| = |3(x+iy)| (3x)2+(3y-1)2 = 9(x2+y2)... View Article

For All Complex Numbers Z1 Z2 Satisfying Mod Z1 Equal 12 And Z2 3 4i Equal 5 The Min Value Of Z1 Z2 Is

Solution: Given |z1|= 12 (circle 1) |z2 - 3 - 4i| = 5 (circle 2) Min |z1-z2| = 12-10 = 2 Hence option (4) is the answer.... View Article

If Mod Z Plus 4 Less Then Or Equal 3 Then The Maximum Value Of Z Plus 1 I

Solution: Given |z + 4| ≤ 3 |z + 1| = |z + 4-3| = |z + 4|+|-3| ≤ 3+3 ≤ 6 Hence option (3) is the answer.... View Article

The Equation Of The Locus Of Z Such That Z I By Z I 2 Where Z Equal X Plus Iy Is A Complex Number Is

Solution: |(z-i)/(z+i)| = 2 |(z-i)| = 2|(z+i)| Take z = x+iy |(x+(y-1)i| = 2|(x+(y+1)i| x2+(y-1)2 = 4(x2+(y+1)2) x2+y2-2y+1 =... View Article

What Is The Cosine Inverse Of 0

Inverse functions in trigonometry are used to get the angle with any of the trigonometry ratios. Cosine inverse is usually written as arccos(x)... View Article

What Is A In A Parabola

A parabola is a graph that is U shaped. It is a conic section which is made by the intersection of a cone and a plane. y = ax2+bx+c is the... View Article

What Does Xy Plane Mean

XY plane in two dimensions is used to denote an ordered pair such as (x, y) in which former is called abscissa, while latter is known as... View Article

What Is The Derivative Of Sum Of Two Functions

Derivative of the sum of two functions is the sum of their derivatives. The derivative of a sum of 2 functions = Derivatives of first function +... View Article

What Is The Probability Of A Or B

The probability theory is a branch of Mathematics that deals with the chances of occurrence of the events. In probability theory, we usually find... View Article

Why Is Diamond So Strong

In diamond, the outer shell of each carbon atom has 4 electrons and again these electrons are shared with 4 other carbon atoms by covalent bonds.... View Article

What Quadratic Means

Quadratic is relating to the second power. In Mathematics, the term quadratic describes something that pertains to terms of the second degree... View Article

How Do You Find The Conjugate

Complex numbers having the same real part and imaginary parts of opposite signs in a complex pair is defined as complex conjugates. Let z be a... View Article

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