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What Does A Dot Product Represent

Dot product of two vectors represents the product of the magnitude of the one vector with the resolved component of the second vector and in the... View Article

What Is Equilibrium And Its Types

Equilibrium is a state in which neither the internal energy nor the movement of body changes with time. It has three different types, they are:... View Article

How Do You Convert Sin To Degrees

Since, we know, in a right triangle, sine of an angle is equal to the opposite to the angle and hypoteuse side. Let the angle be θ. Therefore,... View Article

What Is The Value Of Sin Theta

In a right-angled triangle, the value of sin theta is equal to the ratio of opposite side to theta and hypotenuse. Sin θ = Opposite side to... View Article

The Statement A Ib Less Than C Id Is True For

(1) a2+b2 = 0 (2) b2+c2 = 0 (3) a2+c2 = 0 (4) b2+d2 = 0 Solution: For a+ib < c+id to be true, they should be real numbers that are... View Article

The Least Positive Integer N Which Will Reduce I 1 By I 1 N To A Real Number Is

Solution: [(i-1)/(i+1)]n = [(i-1)(i-1)/(i+1)(i-1)]n = (i2-2i+1)/(-1-1) =-1-2i+1)/-2 = -2i/-2 = i i2 = -1 (-1 is a real number) So... View Article

I Power 2 I Power 4 Plus I 6 2n 1 Terms

Solution: i2+i4+i6 +...(2n+1) = -1+1-1+1….-1 (odd no. of terms) = -1 Hence option (4) is the answer.... View Article

1 Plus I Square I Power 4 I 2n Is

Solution: i2 = -1 i4 = 1 i6 = -1 Put n = 3 1+i2+i4+i6 = 1-1+1-1 = 0 Put n = 4 1+i2+i4+i6 +i8= 1-1+1-1 +1 = 1 The value will vary... View Article

If 2x Equal 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 = (30i-16)/4 Substitute x3, x2 in... View Article

The Value Of 1 I 5 1 I 5

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

If 1 I By 1 I3 1 I By 1 I3 X Iy

Solution: [(1+i)/(1-i)]3 - [(1-i)/(1+i)]3 = x+iy = [(1+i)2/(1-i2)]3-[(1-i)2/(1-i2)]3 = [(1+2i+i2)/(1+1)]2-[(1-2i+i2)/(1+1)]3 =... View Article

If 1 I N 2 N Then N Is Equal To

Solution: (1-i)n = 2n+0i If two complex numbers are equal, their moduli are also equal. |(1-i)n| = |2n| |1-i|n = |2n| √(12+(-1)2]n = 2n... View Article

If 1 I 1 I M 1 Then Least Integral Value Of M Is

Solution: [(1+i)/(1-i)]m = 1 Multiply numerator and denominator with(1+i) [(1+i)(1+i)/(1-i)(1+i)]m = 1 [(1+i)2/(1+1)]m = 1 [(1+2i-1)/2)]m... View Article

If N Is A Positive Integer Then Which Of The Following Relations Is False

(1) i4n = 1 (2) i4n-1 = i (3) i4n+1 = i (4) i-4n = 1 Solution: Put n = 1 and check the given options. i4n-1 = i3 = i2 i = -1(i) = -i... View Article

Root 2 Root 3 Is Equal To

Solution: We know √-1 = i √2√-3 = √2√3√-1 = √6i Hence option (3) is the answer.... View Article

The Real Part Of 1 I I Is

(1) e-π/4 cos (½ log 2) (2) -e-π/4 sin (½ log 2) (3) eπ/4 cos (½ log 2) (3) e-π/4 sin (½ log 2) Solution: Let z = (1-i)-i On taking log... View Article

If Z 1 Iroot 3 By Root 3 I Then Bar Z 100 Lies In

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

The Amplitude Of E Power E I Theta Is Equal To

Solution: ecos θ-i sin θ = ecos θ e -i sin θ = ecos θ|e -i sin θ| = ecos θ Hence option (3) is the answer.... View Article

Real Part Of E Ei Theta Is

(1) ecos θ( cos (sin θ) (2) ecos θ( cos (cos θ) (3) esin θ( sin (cos θ) (4) esin θ( sin (sin θ) Solution: ecos θ (ei sin θ) = ecos θ(... View Article

If 1 I Root 3 9 A Ib Then B Is Equal To

Solution: (1+i√3)9 = a+ib = 29 [(½)+(√3/2)i ]9 = 29 [ cos π/3 + i sin π/3]9 Apply de moivre's theorem = 29 [ cos 9π/3 + i sin 9π/3] =... View Article

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