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What Are Matrices In Math

In Maths, a matrix is defined as a rectangular array of numbers, which are arranged in rows and columns. Each number in the array is called the... View Article

What Is Heat Engine What Are Some Examples From Everyday Life Of Heat Engines

A heat engine is a device that converts heat to work. It takes heat from a reservoir then does work such as lifting weight and moving a piston... View Article

How Do You Find The Probability Of Two Independent Events

In probability, independent events are the events that are not affected by previous events. To calculate the probability of two independent... View Article

What Does Inverse Mean

In Mathematics, the word “Inverse” refers to the opposite operation. It means that the operation reverses the process of other... View Article

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