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Syllabus

what is (a+b+c)whole square

sir how to solve quadratic inequalities by wavy curve method

Q Find the square root of the complex number 5 -12i.(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.

prove 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 ???

^{24}+(1/i)^{26}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

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

if z=4+3i then find modulus and multiplication inverse of z

find sqrt(1-i)

Answer is 11 pi/12

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

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

1/i^(4m+k), m belongs to N

if (x+iy)

^{3}= u+iv, then show that u/x +v/y = 4(x^{2}- y^{2})^{2}+a^{3}+a^{4}if z is a complex number and |z|=1 then prove that z-1/z+1 is a purely imaginary number^{2}^{}-10x+3=0 are alpha and beta^{2}where beta^{2}<1/2 then the equation whose roots are (alpha+ibeta)^{100}and (alpha-ibeta)^{100}is?find 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}if x-iy=underroot [(a-ib)/(c-id)]

prove that(x

^{2}+y^{2})^{2}= a^{2}+b^{2}/c^{2}+d2If 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

_{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}|_{2}+Z_{3}-2Z_{1}/ Z_{3}-Z_{2})is equal is (a) $\pi /4\left(b\right)\pi /2\left(c\right)\pi /3\left(d\right)\pi /6$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?Solve :-

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

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

Solve :-

x^{2}-(7 - i) x + (18 - i) = 0 over C.ANURAG.^{99}If x + iy = a + ib/a- ib, show that x

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

^{2/3}+ 2^{1/3}, then find the value of x^{3 }- 6x^{2}+ 6x.Prove that (1 + i)

^{5}(1 + 1/i)^{5}= 32if Z is a complex number such that Z-1 / Z+1 is purely imaginary.prove that |Z|=1

if one vertex of an equilateral triangle is 1+i and centroid is at origin, then find the other two vertices of triangle?

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-iaFind all pairs (x,y) of real numbers such that

_{16}x^{2}+y +_{16}x+y^{2}=1.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

^{2}+ 2px + q =0 and x^{2}+ 2qx + p = 0 differ by a constant, show tha p + q + 1 =0.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??Q.Find the modulus and amplitude of the complex no. and show it in polar form

1+root3 iyota.

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

x

^{2}/y^{2 }+ y^{2}/x^{2 }+ 1/2i (x/y+y/x) + 31/16Q. If p+iq = (a-i)

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

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

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

how to find the multiplicative inverse of 2-3i

prove the triangle inequality: IZ1 - z2I <or equal to Iz1I+Iz2I

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

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 (1-i/1+i)

^{500}=a+ib, find the values of a and bEvaluate :

2x

^{3}+2x^{2}-7x+72,when x=(3-5i)/29. Express i

^{9}+ i^{10}+ i^{11}+ i^{12}in the form of a+ibif a =cosA+isinA,find the value of (1+a)/(1-a)

Solve this :$13.\mathrm{If}\left|\mathrm{z}-\mathrm{i}\right|\le 5\mathrm{and}{\mathrm{z}}_{1}=5+3\mathrm{i}(\mathrm{where},\mathrm{i}=\sqrt{-1}),\mathrm{then}\mathrm{greatest}\mathrm{and}\mathrm{the}\mathrm{least}\mathrm{values}\mathrm{of}\left|\mathrm{iz}+{\mathrm{z}}_{1}\right|\mathrm{are}\phantom{\rule{0ex}{0ex}}\left(\mathrm{a}\right)7\mathrm{and}3\left(\mathrm{b}\right)9\mathrm{and}1\left(\mathrm{c}\right)10\mathrm{and}0\left(\mathrm{d}\right)\mathrm{None}\mathrm{of}\mathrm{these}$

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.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) = 0find the square root of

What is the angle between vectors z and -iz ?

If (1+i/1-i)

^{3}- (1-i/1+i)^{3}= x+iy, then find (x,y)^{2}-2iz+2c(1+i)=0.. the value of 'b' for which equationsQx

^{2}+bx-1=0x

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

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

2)36

if 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)square root of -15-18i

^{10 }+i^{100-}-i^{1000}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.z= -16/1+i√3 into polar form.If iZ

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