Question and Answers Forum

OthersQuestion and Answers: Page 101

Question Number 51837 Answers: 1 Comments: 1

Question Number 51721 Answers: 1 Comments: 0

Find the range of value of x given that: ∣x + i∣ ≥ (1/x)

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{range}\:\mathrm{of}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x}\:\mathrm{given}\:\mathrm{that}:\:\:\:\:\:\mid\mathrm{x}\:+\:\mathrm{i}\mid\:\geqslant\:\frac{\mathrm{1}}{\mathrm{x}} \\ $$

Question Number 51673 Answers: 0 Comments: 1

Question Number 51643 Answers: 2 Comments: 0

If ∣z∣ = 1, prove that ((z − 1)/(z^− − 1)) (z ≠ 1) is a pure imaginary

$$\mathrm{If}\:\:\:\mid\mathrm{z}\mid\:=\:\mathrm{1},\:\:\:\:\mathrm{prove}\:\mathrm{that}\:\:\:\:\:\frac{\mathrm{z}\:−\:\mathrm{1}}{\overset{−} {\mathrm{z}}\:−\:\mathrm{1}}\:\:\:\:\:\:\left(\mathrm{z}\:\neq\:\mathrm{1}\right)\:\:\:\mathrm{is}\:\mathrm{a}\:\mathrm{pure}\:\mathrm{imaginary} \\ $$

Question Number 51630 Answers: 1 Comments: 4

Question Number 51628 Answers: 0 Comments: 2

Question Number 51621 Answers: 0 Comments: 6

Question Number 51571 Answers: 1 Comments: 0

If α − jβ = (1/(a − jb)) , where α, β, a, b are real, express b in terms of α, β Answer: ((− β)/(α^2 + β^2 − 2α + 1))

$$\mathrm{If}\:\:\:\alpha\:−\:\mathrm{j}\beta\:\:=\:\:\frac{\mathrm{1}}{\mathrm{a}\:−\:\mathrm{jb}}\:\:,\:\:\:\:\:\:\mathrm{where}\:\:\:\alpha,\:\beta,\:\mathrm{a},\:\mathrm{b}\:\:\mathrm{are}\:\mathrm{real},\:\mathrm{express}\:\:\mathrm{b}\:\:\mathrm{in}\:\mathrm{terms} \\ $$$$\mathrm{of}\:\:\alpha,\:\beta\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{Answer}:\:\:\:\:\:\:\:\:\:\:\frac{−\:\beta}{\alpha^{\mathrm{2}} \:+\:\beta^{\mathrm{2}} \:−\:\mathrm{2}\alpha\:+\:\mathrm{1}} \\ $$

Question Number 51448 Answers: 0 Comments: 3

Question Number 51420 Answers: 2 Comments: 0

∫ (e^(3x) /(1 + e^x )) dx

$$\int\:\:\frac{\mathrm{e}^{\mathrm{3x}} }{\mathrm{1}\:+\:\mathrm{e}^{\mathrm{x}} }\:\mathrm{dx} \\ $$

Question Number 51389 Answers: 1 Comments: 2

Question Number 51360 Answers: 0 Comments: 0

Question Number 51321 Answers: 1 Comments: 0

A B C D is a parallelogram on the Argand plane. The affixes of A, B, C are 8 + 5i, − 7 − 5i, − 5 + 5i respectively . Find the affix of D

$$\mathrm{A}\:\mathrm{B}\:\mathrm{C}\:\mathrm{D}\:\:\mathrm{is}\:\mathrm{a}\:\mathrm{parallelogram}\:\mathrm{on}\:\mathrm{the}\:\mathrm{Argand}\:\mathrm{plane}.\:\mathrm{The}\: \\ $$$$\mathrm{affixes}\:\mathrm{of}\:\:\mathrm{A},\:\mathrm{B},\:\mathrm{C}\:\:\mathrm{are}\:\:\:\mathrm{8}\:+\:\mathrm{5i},\:\:−\:\mathrm{7}\:−\:\mathrm{5i},\:\:−\:\mathrm{5}\:+\:\mathrm{5i}\:\:\mathrm{respectively} \\ $$$$.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{affix}\:\mathrm{of}\:\:\mathrm{D} \\ $$

Question Number 51320 Answers: 1 Comments: 0

The points A, B, C represent the complex numbers z_1 , z_2 , z_3 respectively. And G is the centroid of the triangle A B C, if 4z_1 + z_2 + z_3 = 0, show that the origin is the mid point of AG.

$$\mathrm{The}\:\mathrm{points}\:\mathrm{A},\:\mathrm{B},\:\mathrm{C}\:\:\mathrm{represent}\:\mathrm{the}\:\mathrm{complex}\:\mathrm{numbers}\:\:\mathrm{z}_{\mathrm{1}} ,\:\mathrm{z}_{\mathrm{2}} ,\:\mathrm{z}_{\mathrm{3}} \: \\ $$$$\mathrm{respectively}.\:\mathrm{And}\:\mathrm{G}\:\mathrm{is}\:\mathrm{the}\:\mathrm{centroid}\:\mathrm{of}\:\mathrm{the}\:\mathrm{triangle}\:\mathrm{A}\:\mathrm{B}\:\mathrm{C},\:\:\mathrm{if} \\ $$$$\mathrm{4z}_{\mathrm{1}} \:+\:\mathrm{z}_{\mathrm{2}} \:+\:\mathrm{z}_{\mathrm{3}} \:\:=\:\:\mathrm{0},\:\:\mathrm{show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{origin}\:\mathrm{is}\:\mathrm{the}\:\mathrm{mid}\:\mathrm{point}\:\mathrm{of}\:\:\mathrm{AG}. \\ $$

Question Number 51316 Answers: 0 Comments: 2

Question Number 51314 Answers: 0 Comments: 1

Question Number 51312 Answers: 0 Comments: 1

Question Number 51307 Answers: 0 Comments: 3

Question Number 51284 Answers: 1 Comments: 1

If x is real, show that (2 + j)e^((1 + j3)x) + (2 − j)e^((1 − j3)x) is also real

$$\mathrm{If}\:\:\boldsymbol{\mathrm{x}}\:\mathrm{is}\:\mathrm{real},\:\mathrm{show}\:\mathrm{that}\:\:\left(\mathrm{2}\:+\:\mathrm{j}\right)\mathrm{e}^{\left(\mathrm{1}\:+\:\mathrm{j3}\right)\boldsymbol{\mathrm{x}}} \:+\:\left(\mathrm{2}\:−\:\boldsymbol{\mathrm{j}}\right)\boldsymbol{\mathrm{e}}^{\left(\mathrm{1}\:−\:\boldsymbol{\mathrm{j}}\mathrm{3}\right)\boldsymbol{\mathrm{x}}} \\ $$$$\mathrm{is}\:\mathrm{also}\:\mathrm{real} \\ $$

Question Number 51250 Answers: 1 Comments: 0

Given that z_1 = R_1 + R + jωL ; z_2 = R_2 ; z_3 = (1/(jωC_3 )) and z_4 = R_4 + (1/(jωC_4 )) and also that z_1 z_3 = z_2 z_4 , express R and L in terms of the real constants R_1 , R_2 , R_4 , C_3 and C_4 Answer: R = ((R_2 C_3 − R_1 C_4 )/C_4 ) , L = R_2 R_4 C_3

Question Number 51248 Answers: 1 Comments: 0

If ((R_1 + jωL)/R_3 ) = (R_2 /(R_4 − j (1/(ωC)))) , where R_1 , R_2 , R_3 , R_4 , ω, L and C are real , show that L = ((C R_2 R_3 )/(ω^2 C^2 R_4 ^2 + 1))

$$\mathrm{If}\:\:\:\:\:\frac{\mathrm{R}_{\mathrm{1}} \:+\:\mathrm{j}\omega\mathrm{L}}{\mathrm{R}_{\mathrm{3}} }\:\:=\:\:\frac{\mathrm{R}_{\mathrm{2}} }{\mathrm{R}_{\mathrm{4}} \:−\:\mathrm{j}\:\frac{\mathrm{1}}{\omega\mathrm{C}}}\:\:,\:\:\:\mathrm{where}\:\:\mathrm{R}_{\mathrm{1}} ,\:\mathrm{R}_{\mathrm{2}} ,\:\mathrm{R}_{\mathrm{3}} ,\:\mathrm{R}_{\mathrm{4}} ,\:\omega,\:\mathrm{L}\:\mathrm{and}\:\mathrm{C} \\ $$$$\mathrm{are}\:\mathrm{real}\:,\:\:\mathrm{show}\:\mathrm{that}\:\:\:\:\mathrm{L}\:=\:\frac{\mathrm{C}\:\mathrm{R}_{\mathrm{2}} \mathrm{R}_{\mathrm{3}} }{\omega^{\mathrm{2}} \mathrm{C}^{\mathrm{2}} \mathrm{R}_{\mathrm{4}} ^{\mathrm{2}} \:+\:\mathrm{1}} \\ $$

Question Number 51199 Answers: 0 Comments: 0

Question Number 50892 Answers: 3 Comments: 0

solve the equation tan 3θcotθ+1=0 for 0≤θ≤180 b)show that if cos 2θ is not zero then cos 2θ+sec 2θ=2[((cos^4 θ+sin^4 θ)/(cos^4 θ−sin^4 θ))] c)find the limit of ((tan (θ/3))/(3θ)) as θ→0

$${solve}\:{the}\:{equation} \\ $$$$\mathrm{tan}\:\mathrm{3}\theta{cot}\theta+\mathrm{1}=\mathrm{0}\:{for} \\ $$$$\mathrm{0}\leqslant\theta\leqslant\mathrm{180} \\ $$$$\left.{b}\right){show}\:{that}\:{if}\:\mathrm{cos}\:\mathrm{2}\theta\:{is}\:{not}\:{zero} \\ $$$${then} \\ $$$$\mathrm{cos}\:\mathrm{2}\theta+\mathrm{sec}\:\mathrm{2}\theta=\mathrm{2}\left[\frac{\mathrm{cos}\:^{\mathrm{4}} \theta+\mathrm{sin}\:^{\mathrm{4}} \theta}{\mathrm{cos}\:^{\mathrm{4}} \theta−\mathrm{sin}\:^{\mathrm{4}} \theta}\right] \\ $$$$\left.{c}\right){find}\:{the}\:{limit}\:{of} \\ $$$$\frac{\mathrm{tan}\:\frac{\theta}{\mathrm{3}}}{\mathrm{3}\theta}\:{as}\:\theta\rightarrow\mathrm{0} \\ $$$$ \\ $$

Question Number 50835 Answers: 1 Comments: 1

Question Number 50796 Answers: 1 Comments: 1

∫1/(1+x^4 )dx=

$$\int\mathrm{1}/\left(\mathrm{1}+{x}^{\mathrm{4}} \right){dx}= \\ $$

Question Number 50764 Answers: 0 Comments: 2

Pg 96 Pg 97 Pg 98 Pg 99 Pg 100 Pg 101 Pg 102 Pg 103 Pg 104 Pg 105

Contact: info@tinkutara.com