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Syllabus

what is (a+b+c)whole square

(1+x+xshow that^{2})^{n}= a_{0 +}a_{1}x +a_{2}x^{2}+ a_{3}x^{3}+ .......+ a_{2n}x^{2n},a_{0}+a_{3}+a_{6}+ .......... = 3^{n-1}sir how to solve quadratic inequalities by wavy curve method

_{1}|=1 ,|z_{2}|=2 ,|z_{3}|=3 and |9z_{1}z_{2}+ 4z_{1}z_{3}+ z_{2}z_{3}|=12 then find |z_{1}+ z_{2}+ z_{3}|Q Find the square root of the complex number 5 -12i.if z is a complex number and |z|=1 then prove that z-1/z+1 is a purely imaginary numberprove that

cosA +cosB +cosC +cos(A+B+C) = 4cos((A+B) / 2)cos((B+C) / 2)cos((C+A) / 2)

A)x=-2

B)x=2

C)y=-2

D)y=1

Find the modulus and argument of 1 + 2 i / 1 - 3 i ???

if z is a complex number satisfying z^4+z^3+2z^2+z+1=0,then find the value of |z| conjugte

if the ratio of the roots of the equation x

^{2}+px+q=0 is equal to the ratio of the roots of the equation x^{2}+lx+m=0, prove that mp^{2}=ql^{2}Show that if x is real , the expression x2-bc/ 2x-b-c has no real value between b and c.

Express in polar form 1 + 2i/1-3i

Solve for z, the equation |z|+ z = 2 + i

If (x+iy)^1/3 =(a+ib),prove that (x/a+y/b)=4(a^2-b^2)?

if |z-4/z| =2 then what is the maximum value of |z| is equal to

if alpha and beta are 2 different complex numbers with |beta| = 1, then find |beta-alpha/1-bar alpha*beta|

find sqrt(1-i)

If z =(x+iy) and w =( 1 - iz) / (z - 1) such that | w | = 1 then show that z is purely real .

a,b,c are three distinct real numbers and they are in G.P. If a+b+c = xb, then prove that x<-1 or x>3.

if (x+iy)

^{3}= u+iv, then show that u/x +v/y = 4(x^{2}- y^{2})find the value of x and y if (1+i)x-2i/3+i + (2-3i)y+i/3-i =i

if x-iy=underroot [(a-ib)/(c-id)]

prove that(x

^{2}+y^{2})^{2}= a^{2}+b^{2}/c^{2}+d2_{(m=1 to 15)}Im(z^{2m-1}) at theta = 2^{o}is(A) 1/ sin 2

^{o}^{}(B) 1/ 3sin 2

^{o}(C) 1/ 2sin 2

^{o}(D) 1/ 4sin 2

^{o}Find the value of a for which one root of the quadratic equation (a

^{2}-5a+3)x^{2}+(3a-1)x+2=0 is twice as large as the other.How can we eliminate alpha here? Please solve the problem?SUPPOSE z

_{1 }z_{2 }z_{3 }ARE THE VERTICES OF AN EQUILATERAL TRIANGLE INSCRIBED IN THE CIRCLE / Z / = 2 IF z_{1}= 1 + 3 1/2 ITHEN z

_{2}& z_{3}areSolve :-

x^{2}-(7 - i) x + (18 - i) = 0 over C.ANURAG.if a+b+c=0, prove that the roots of ax^2+bx+c=0 are rational. Hence, show that the roots of (p+q)x^2-2px+(p-q)=0 are rational

Solve :-

2x^{2}- (3+7i) x - (3-9i) = 0ANURAG.solve the system of equation

Re(z

^{2})=0,|z|=2^{}if (x+iy)(2-3i)=4+i then find (x,y)

IF x_{r}=cos pi /2^{r}+ i sin pi/2^{r},then value of x_{1}.x._{2}x_{3}...to infinity isequal to1.1

2.0

3. -1

4.2

If x + iy = a + ib/a- ib, show that x

^{2}+y^{2}=1If x = 2 + 2

^{2/3}+ 2^{1/3}, then find the value of x^{3 }- 6x^{2}+ 6x.if Z is a complex number such that Z-1 / Z+1 is purely imaginary.prove that |Z|=1

If (x + iy) = sqrt [(1+i)/(1-i)],

prove that : x

^{2}+ y^{2}= 1if a

^{2}+ b^{2}=1 , then find the value of 1+b+ia/1+b-ia$\mathbf{5}\mathbf{.}\mathbf{}If\left|z-25i\right|\le 15,\left|maximumarg\left(z\right)-minimumarg\left(z\right)\right|equals:\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\left(A\right)2{\mathrm{cos}}^{-1}(3/5)\left(B\right)2{\mathrm{cos}}^{-1}(4/5)\phantom{\rule{0ex}{0ex}}\left(C\right)\frac{\mathrm{\pi}}{2}+{\mathrm{cos}}^{-1}(3/5)\left(4\right){\mathrm{sin}}^{-1}(3/5)-{\mathrm{cos}}^{-1}(3/5)$

let alpha and beta are the roots of x

^{2}-6x-2=0,with alpha beta . if a_{n}=alpha^{n}-beta^{n }for n=1,then value of a(greater than or equal to one)_{10}-2a_{8}/ 2a_{9 }is??if a+ib= c+i / c-i , where c is real part

prove that

a square + b square =1

and b / a =2c / c square-1

if z1= 1-i and z2= -2+4i find i'm(z1*z2/z1) maths class 11

n n+1 are in power .

if a is not equal to b and a^2=5a -3 , b^2=5b-3, then form the equation whose roots are a/b and b/a

if x

^{2}+x+1=0.then find the value of(x+1/x)^{2}+(x^{2}+1/x^{2})^{2}+(x^{3}+1/x^{3})^{2}+-------------(x^{2}^{7}+1/x^{27})^{2}For the quadratic equation ax2+bx+c+0, find the condition that

(i) one root is reciprocal of other root

(ii) one root is m times the other root

(iii) one root is square of the other root

(iv) one root is nth power of the other root

(v) the roots are in the ratio m:n

Let z1 and z2 be two complex numbers such that z1 + iz2 = 0 and arg (z1z2) = pi.

Find arg (z1).

Q. If p+iq = (a-i)

^{2}/ 2a-i , show that p^{2}+q^{2}= (a^{2}+1)^{2}/ 4a^{2}+1.If

thenx=3+i,?x^{3}-3x^{2}-8x+15=how to find the multiplicative inverse of 2-3i

Express in form of a+ib

(1-i)/(1+i)...

Please help me expert......

if the sum of the roots of the equation ax2 + bx + c = 0 is equal to the sum of the squares of their squares of their reciprocals , then show that bc

^{2}, ca^{2}, ab^{2}are in A.P.If the sum of the roots of the equation x

^{2}-px+q=0 be m times their difference, prove that p^{2}(m^{2}-1)=4m^{2}qfind the smallest positive integer n for which (1+i)^2n =(1-i)^2n

for what real values of a do the roots of the equation x^2-2x-(a^2-1)=0 lie between the roots of the equation x^2-2(a+1)+a(a-1)

Express it in the polar form: (i-1) / (cospi/3) + (isin pi/3).Also Find the arguement and modulus.

express i-39 (iota raised to the power minus 39) in the form of a+ib

if a =cosA+isinA,find the value of (1+a)/(1-a)

Evaluate :

2x

^{3}+2x^{2}-7x+72,when x=(3-5i)/2find the square root of

if z=(3+7i)(p+iq),where p,q are non-zero integers,is purely imaginary then minimum value of |z|^2 is

Show that the roots of (x-b)(x-c) +(x-c)(x-a) +(x-a)(x-b) =0 are real, and that they cannot be equal unless a=b=c.

Provide R.D Sharma solutions of class 11 as it is a common demand by many students

find the complex numbers Z satisfying the equation:- |Z-4| / |Z-8|=1 & |Z-12 | /|Z-8i|=5/3

If (1+i/1-i)

^{3}- (1-i/1+i)^{3}= x+iy, then find (x,y)if a+ib =( (x+i)

^{2}) / (2x^{2}+ 1)prove that a2 +b

^{2}=((x^{2}+ 1)^{2}) / (2x^{2}+1)^{2}solve :(2 + i)x

^{2 }- (5 -i)x + 2(1-i) = 0root( x

^{2 }-3x )= 4x^{2}- 12x - 3 answer: (3+/- root13)/2 or (6+/- 3root5)/4PROVE THAT A REAL VALUE OF x WILL SATISFY THE EQUATION 1 - ix / 1 + ix = a - ib , if a

^{2}+ b^{2}=1 ; where 'a' and 'b' are real.. the value of 'b' for which equationsQx

^{2}+bx-1=0x

^{2}+x+b=0have one root in common is ??

if a+ib/c+id=p+q then prove that p2+q2=a2+b2/c2+d2

If the roots of the equation x

^{2}-2ax+a^{2}+a-3 =0 are less than 3 then find the set of all possible values of a. (ans : -infinity, 2)If [(1-i)/(1+i)]

^{100}=a+ib, then find (a,b)^{2}+ax-3b) *(x^{2}-cx+b) *(x^{2}-dx+2b)=0 has atleast two real roots.Find the least positive integral value of n for which (1+i/1-i)

^{n}is real.1)a=0 , c=0

2)b=0 , c=0

If a+ib = c+i / c-i, where c is real, prove that a

^{2}+ b^{2 }=1 and b/a = 2c / c^{2}-1.^{2}+2(a-1)x+a+5=0 are1.exactly 1 root lies in the interval(1,3)

2.both the roots lie in the interval(1,3)

3.one root is greater than 3 and other is smaller than 1