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Syllabus

what is (a+b+c)whole square

Find Integral values of x for which x

^{2 }+ 19x + 46 is a perfect square?sir how to solve quadratic inequalities by wavy curve method

^{2}-2x+a=6-ax posses equal roots?Q Find the square root of the complex number 5 -12i.Please solve this and explain each step

prove that

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

Q.23. If ${\mathrm{log}}_{a}x$ = 0.3 and ${\mathrm{log}}_{a}3$ = 0.4, then ${\mathrm{log}}_{3}x$ is

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

(x-2) respectively. If R(x) be the remainder when polynomial is divided by x(x - l) (x- 2), then

(A) R(x) is a quadratic polynomial (B) R (x) have real roots

(C) R (x) integer roots (D) R (10) = 132

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

Answer is 11 pi/12

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

Y=

x^{2}+2x-11 2(x-3)

find sqrt(1-i)

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

solve the quadratic equation :

4x

^{4}- 16 x^{3}+ 7x^{2}+ 16 x + 4 = 0If z =(x+iy) and w =( 1 - iz) / (z - 1) such that | w | = 1 then show that z is purely real .

If x is Real , Then (x

^{2}- x + c) / (x^{2}+ x + 2c) can take all real values if:-a) c belongs to [ 0 , 6 ]

b) c belongs to [ -6 , 0 ]

c) c belongs to ( -6 , 0 )

d) None Of These

if (x+iy)

^{3}= u+iv, then show that u/x +v/y = 4(x^{2}- y^{2})express i-39 (iota raised to the power minus 39) in the form of a+ib

if z is a complex number and |z|=1 then prove that z-1/z+1 is a purely imaginary numberfind the value of x and y if (1+i)x-2i/3+i + (2-3i)y+i/3-i =i

(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}(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.

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

prove that(x

^{2}+y^{2})^{2}= a^{2}+b^{2}/c^{2}+d2^{2}-40a+220=0_{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}|ques :: consider the quadrati polynomial f(x) x

^{2 }-4ax+5a^{2}-6aa)find the smallest +ive integral value of 'a' for which f(x) is +ive for every real x

.find the largest distance b/w the roots of the equation f(x)=0

plss ans it soon :P i have test tmrow :(

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?^{29 }+ 1/i^{29}Solve :-

2x^{2}- (3+7i) x - (3-9i) = 0ANURAG.^{2}y and x^{2}+ y + 4i conjugates complexes ?if (x+iy)(2-3i)=4+i then find (x,y)

Solve :-

x^{2}-(7 - i) x + (18 - i) = 0 over C.ANURAG.for what values of x and y are the nos. 3+ix^2y and x^2 + y+ 4i conjugate complexes? plz help..!!

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

^{2}+y^{2}=1pls solve this question.... if (1+2i)(2+3i)(3+4i)= x+iy.Show that x^2 +y^2 =1625.

If 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 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.solve for x and y

(3+i)x +(1-2i)y+7i =0

if a

^{2}+ b^{2}=1 , then find the value of 1+b+ia/1+b-iax+ 2010) (x + a) + 1 = 0 has integral roots is(A) 2008 (B) 2010 (C) 2012 (D) 2014

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

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

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

^{2}/ 2a-i , show that p^{2}+q^{2}= (a^{2}+1)^{2}/ 4a^{2}+1.solve the equation (x+2)(3x+4)(3x+7)(x+3) =2600

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

(1). Express in the form of A + iB :

(alpha + ibeta)

^{x+iy }(2). Find all the real values of (1 + i tan alpha)

^{1 + i tan beta}how to find the multiplicative inverse of 2-3i

Experts please dont give links and answer with detailed steps

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

(A) both roots lie between $-\frac{a}{2}$ and a

(B) both roots are positive

(C) both roots are negative

(D) both roots are imaginary

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.

^{99}Evaluate :

2x

^{3}+2x^{2}-7x+72,when x=(3-5i)/2if a =cosA+isinA,find the value of (1+a)/(1-a)

Express the following polar no.s in polar form

PROVE 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.(A) a > 10 (B) –15 < a < 5 (C) –10 < a < 5 (D) none of these

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.

^{3})+(9-i)+(9+i^{2})1)root 533

2)36

solve :(2 + i)x

^{2 }- (5 -i)x + 2(1-i) = 0find the square root of

If (1+i/1-i)

^{3}- (1-i/1+i)^{3}= x+iy, then find (x,y)Experts!! Please answer!!. How can we find the real values of x & y, if : (x -1 / 3 + i) + (y - 1 / 3 - i) = i????

. the value of 'b' for which equationsQx

^{2}+bx-1=0x

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

root( x

^{2 }-3x )= 4x^{2}- 12x - 3 answer: (3+/- root13)/2 or (6+/- 3root5)/4if a+ib =( (x+i)

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

^{2}=((x^{2}+ 1)^{2}) / (2x^{2}+1)^{2}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)Express sin30+icos30 in polar form.

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.x

^{2}+x++2k (x^{2}-x-1) = 0 is a perfect square for hw many values of k? pls answerIf iZ

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