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Syllabus

what is (a+b+c)whole square

^{4}x/2 + cos^{4}x /3 = 1/5 then(a) tan

^{2}x = 2/3(b) sin

^{8}x / 8 + cos^{8}x / 27 = 1 / 125(c) tan

^{2}x =1/3(d)sin

^{8}x / 8 + cos^{8}x / 27 = 2 / 125sir how to solve quadratic inequalities by wavy curve method

If Every Pair from among the equations x

^{2 }+ px+ qr =0 , x^{2}+ qx + rp = 0 and x^{2 }+ rx + pq = 0 has a common root, then the sum of the three common roots is????OPTIONS:-

a) 2(p+q+r)

b) p+q+r

c) -(p+q+r)

d) pqr

Q Find the square root of the complex number 5 -12i.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}qprove that

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

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

^{2}+(aw+bw^{2})^{2}+(aw^{2}+bw)^{2}= 6abif 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}(a+bw+cw

^{2})/(b+cw+aw^{2}) +(a+bw+cw^{2})/(c+aw+w^{2}) is,1). 1

2). -1

3). 2

4). -2

where, w represents omega.

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

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

^{x}+ (4-√15)^{x}= 62 then x isfind sqrt(1-i)

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

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

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

if (x+iy)

^{3}= u+iv, then show that u/x +v/y = 4(x^{2}- y^{2})Q. If p+iq = (a-i)

^{2}/ 2a-i , show that p^{2}+q^{2}= (a^{2}+1)^{2}/ 4a^{2}+1.find the value of x and y if (1+i)x-2i/3+i + (2-3i)y+i/3-i =i

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 z is a complex number and |z|=1 then prove that z-1/z+1 is a purely imaginary number^{3}+ 16x^{2}- 9x - 36 = 0 given that sum of two of its roots is zero are ?(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}for which the quadratic equationahas integral roots(x + a)(x + 1991) + 1 = 0if x-iy=underroot [(a-ib)/(c-id)]

prove that(x

^{2}+y^{2})^{2}= a^{2}+b^{2}/c^{2}+d2find the condition that the ratio between the roots of the eqn. ax

^{2}+bx+c=0 may be m:n.x^{2}– 3 sin αx– 2 cos^{2}α = 0 then α lies in the interval(1)$\left(0,\frac{\pi}{2}\right)$ (2) $\left(\frac{\pi}{12},\frac{\pi}{2}\right)$ (3) $\left(\frac{\pi}{6},\frac{5\pi}{6}\right)$ (4) $\left(\frac{\pi}{6},\frac{\pi}{2}\right)\cup \left(\frac{\pi}{2},\frac{5\pi}{6}\right)$

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?the argument of 1- i root 3 / 1 + 1 root 3 is

/32/34/3-2/3/6plz wid stEps i need it 2day itself.....

Solve :-

2x^{2}- (3+7i) x - (3-9i) = 0ANURAG.PLEASE NOTE w= OMEGA

x=a+b

y=aw+bw

^{2}^{2}+bwprove that 1. x+y+z=0

2. x

^{2}+y^{2}+z^{2}=6ab3. xyz=a

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

Solve :-

x^{2}-(7 - i) x + (18 - i) = 0 over C.ANURAG.(2+i root of 3)

^{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 the equation x

^{2 }+ abx + c = 0 & x^{2 }+ acx + v = 0, have a common root, prove that the other roots satisfy the equation x^{2 }- a(b + c)x + a^{2}bc = 0.if Z is a complex number such that Z-1 / Z+1 is purely imaginary.prove that |Z|=1

find the real part of (1-i) ^-i

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 a

^{2}+ b^{2}=1 , then find the value of 1+b+ia/1+b-iaif 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

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 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}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

find the square root of

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

^{3}+ 3x^{2}- 9x + c is of the form (x-a)^{2}(x-b) then find chow to find the multiplicative inverse of 2-3i

IF z_{1}=2+4i and z_{2}=3-i show that |2z_{1}-z_{2}|=2|z_{1}|^{2}+4|z_{2}|^{2}+2 where i^{2}=-1express i-39 (iota raised to the power minus 39) in the form of a+ib

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

^{2}>= 4ac for the eqn ax^{4}+ bx^{2}+ c =0 then all the root of the eqnwill be real if ............. ?ans.

i) b < 0 , a > 0 , c > 0

ii) b > 0 , a < 0, c < 0

find the smallest positive integer n for which (1+i)^2n =(1-i)^2n

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

Evaluate :

2x

^{3}+2x^{2}-7x+72,when x=(3-5i)/2PROVE 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.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.

solve :(2 + i)x

^{2 }- (5 -i)x + 2(1-i) = 0If (x + iy) = sqrt [(1+i)/(1-i)],

prove that : x

^{2}+ y^{2}= 1. the value of 'b' for which equationsQx

^{2}+bx-1=0x

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

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}Find the value of {i}107 + {i]112 + {i}117 + {i}122

(107,112,117,122 are in the power of i )

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

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)$\frac{{b}^{2}-ac}{{a}^{2}}=\frac{{B}^{2}-AC}{{A}^{2}}$

if (1-i/1+i)

^{500}=a+ib, find the values of a and bIf a+ib = c+i / c-i, where c is real, prove that a

^{2}+ b^{2 }=1 and b/a = 2c / c^{2}-1.root(5+12i) + root(5-12i)/ root(5+12i) - root(5-12i) =

1. -3/2 i 2. 3/2i

3. -3/2 4. 3/2

If iZ

^{3}+ Z^{2 }- Z + i = 0 ' then show that mode of Z = 1