Archives

How Do You Find The Geometric Mean And Harmonic Mean

In Mathematics, geometric mean and harmonic mean are the two different types of mean to calculate the average of the given values. The procedure... View Article

Let Z 11 3i 1+I If A Is Real Number Such That Z Ia Is Real Then The Value Of A Is

Solution: Given z = (11-3i)/(1+i) Multiply numerator and denominator with (1-i) z = (11-3i)(1-i)/(1+i)(1-i) = (11-3i-11i-3)/(1+1) =... View Article

If Z Root 3 By 2 I 2 5 Plus Root 3 2 I 2 5 Then

Solution: Given z = (√3/2 +i/2)5+(√3/2 -i/2)5 = (cos π/6 +i sin π/6)5+(cos π/6 -i sin π/6)5 = 2 cos 5π/6 =... View Article

The Complex Numbers Z X Iy Which Satisfy The Equation Z 5i Z+5i 1 Lie On

If 2x 3 5i Then The Value Of 2x 3 2x 2 7x 72 Is

Solution: Given 2x = 3+5i x = (3+5i)/2 x3 = (27+135i-225-125i)/8 = (-198+10i)/8 x2 = (9-25+30i)/4 x2 = (-16+30i)/4 2x3 + 2x2 - 7x +72 =... View Article

If Z Is A Complex Number Such That The Imaginary Part Of Z Is Non Zero And A Z 2 Z 1 Is Real Then A Cannot Take The Value

Solution: Given a = z2+z+1 z2+z+1−a = 0 If solution is not real then b2-4ac<0. 1-4(1-a)<0 1-4+4a <0 -3+4a<0 4a<3... View Article

Argument Of Complex Number 1 3i 2 I Is

Solution: Let z = (-1-3i)/(2+i) = (-1-3i)(2-i)/(2+i)(2-i) = (-2-6i+i-3)/5 = (-5-5i)/5 = (-1-i) Put z = r cos θ+i r sin θ r cos... View Article

If Z 1 Z 2 Z 1 Z Then Find Arg Z 1 Z 2

Solution: Consider z1 = x1+iy1 z2 = x2+iy2 We have |Z1 + Z2| = |Z1| + |Z2| √((x1+x2)2+(y1+y2)2 = √(x12+y12)+√(x22+y22)... View Article

The Product Of All Values Of Cos Alpha I Sin Alpha 3 Is

Solution: (cosα + i sinα)3/5 = cos(3α/5)+i sin (3α/5) Product = (cos(3α/5)+i sin (3α/5))(cos... View Article

The Imaginary Part Of 1 I 2 I 2i 1

Solution: (1+i)2/i(2i-1) = (1+i)2/(-2-i) = (1+i)2 (-2+i)/(-2-i)(-2+i) = (1+i)2 (-2+i)/(4--1) = (1+i)2 (-2+i)/5 = (1+2i-1)(-2+i)/5 =... View Article

The Point 4 1 Undergoes The Following Three Transformations Successively

Solution: When the point (4,1) undergoes reflection, it becomes (1,4) After translation through a distance of 2 units (1+4)+(2,0) = (3,4) After... View Article

If Z 8 Z 8 16 Where Z Is A Complex Number Then The Point Z Will Lie On

Solution: Given |z + 8| + |z - 8|= 16 Let z = x+iy |x+iy+8|+|x-iy-8| = 16 √(x+8)2+y2 = 16-√((x-8)2+y2) x2+64+16x+y2 =... View Article

If Magnitude Of A Complex Number 4 3i Is Tripled And Is Rotated Anticlockwise By An Angle Pi Then Resulting Complex Number Would Be

Solution: |4-3i| = √(42+32) = √25 = 5 When tripled, magnitude = 3(5) = 15 (eiπ )3(4-3i) = (cos π+i sin π)(12-9i) =... View Article

The Point In The Set Z Belongs C Arg Z 2 By Z 6i Equal Pi By 2 Where C Denotes The Set Of All Complex Number Lie On The Curve Which Is

Solution: Given arg ((z-2)/(z-6i) = π/2 Arg (z-2)-arg(z-6i) = π/2 z = x+iy arg ((x-2)+iy) - arg(x+(y-6)i = π/2 = tan -1(y/x-2) -... View Article

Archives

How Do You Find The Geometric Mean And Harmonic Mean

Let Z 11 3i 1+I If A Is Real Number Such That Z Ia Is Real Then The Value Of A Is

If Z Root 3 By 2 I 2 5 Plus Root 3 2 I 2 5 Then

The Complex Numbers Z X Iy Which Satisfy The Equation Z 5i Z+5i 1 Lie On

If 2x 3 5i Then The Value Of 2x 3 2x 2 7x 72 Is

If Z Is A Complex Number Such That The Imaginary Part Of Z Is Non Zero And A Z 2 Z 1 Is Real Then A Cannot Take The Value

Argument Of Complex Number 1 3i 2 I Is

If Z 1 Z 2 Z 1 Z Then Find Arg Z 1 Z 2

The Product Of All Values Of Cos Alpha I Sin Alpha 3 Is

The Imaginary Part Of 1 I 2 I 2i 1

The Point 4 1 Undergoes The Following Three Transformations Successively

If Z 8 Z 8 16 Where Z Is A Complex Number Then The Point Z Will Lie On

If Magnitude Of A Complex Number 4 3i Is Tripled And Is Rotated Anticlockwise By An Angle Pi Then Resulting Complex Number Would Be

If Z X Iy Then Area Of The Triangle Whose Vertices Are Points Z Iz Z Iz Is

The Locus Of The Point Z X Iy Satisfying The Equation Z 1 1 1 Is Given By

If Im Z 1 2z 1 4 Then Locus Of Z Is

If Z 2 1 Z 2 1 Then Z Lies On

If The Complex Numbers Z1 Z2 Z3 Are In An Ap Then They Lie On

The Region Of The Argand Diagram Defined By Mod Z 1 Plus Mod Z Plus 1 Less Than Equal To 4 Is An

The Point In The Set Z Belongs C Arg Z 2 By Z 6i Equal Pi By 2 Where C Denotes The Set Of All Complex Number Lie On The Curve Which Is

FREE TEXTBOOK SOLUTIONS