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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.
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 ???
if the ratio of the roots of the equation x2+px+q=0 is equal to the ratio of the roots of the equation x2+lx+m=0, prove that mp2=ql2
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)?
Find the modulus and argument of complex number z=(1+i)^13/(1-i) ^7
FIND THE MODULUS OF (1+7i) / (2-i)2
if alpha and beta are 2 different complex numbers with |beta| = 1, then find |beta-alpha/1-bar alpha*beta|
pls solve this question.... if (1+2i)(2+3i)(3+4i)= x+iy.Show that x^2 +y^2 =1625.
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(x2 - y2)
if z is a complex number and |z|=1 then prove that z-1/z+1 is a purely imaginary number
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(x2+y2)2= a2+b2/c2+d2
If 1,w,w2 are the cube roots of unity show that
(a+bw+cw2 )3 + (a+bw2 +cw)3 = (2a-b-c) (2b-c-a) (2c-a-b)
If 3 = a+ib prove that a2+b2 = 4a-3
2 + cos(theta) + i sin(theta)
Find the value of a for which one root of the quadratic equation (a2-5a+3)x2+(3a-1)x+2=0 is twice as large as the other.How can we eliminate alpha here? Please solve the problem?
give the geometric representation of x=3 in 1)one variable 2)two variable
Solve :- 2x2 - (3+7i) x - (3-9i) = 0
if cos theta =(root3 - 1)/(2 root 2) and sin theta =(root3+1)/(2 root 2), then what is the arguement
if (x+iy)(2-3i)=4+i then find (x,y)
Solve :- x2 -(7 - i) x + (18 - i) = 0 over C.
express i-39 (iota raised to the power minus 39) in the form of a+ib
If x + iy = a + ib/a- ib, show that x2+y2=1
If (x + iy) = sqrt [(1+i)/(1-i)],
prove that : x2 + y2 = 1
If x = 2 + 22/3+ 21/3, then find the value of x3 - 6x2 + 6x.
if Z is a complex number such that Z-1 / Z+1 is purely imaginary.prove that |Z|=1
If alpha, beta are the roots of ax2+bx+c=0, find the values of:
i. (aplha/beta - beta/alpha)2
ii. alpha3/beta + beta3/alpha
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 bc2 , ca2 , ab2 are in A.P.
if a2 + b2 =1 , then find the value of 1+b+ia/1+b-ia
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
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 x2-6x-2=0,with alpha beta . if an=alphan-betan for n=(greater than or equal to one)1,then value of a10-2a8/ 2a9 is??
if a+ib= c+i / c-i , where c is real part
a square + b square =1
and b / a =2c / c square-1
Show that if x is real , the expression x2-bc/ 2x-b-c has no real value between b and c.
Q. If p+iq = (a-i)2 / 2a-i , show that p2+q2 = (a2+1)2 / 4a2+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
Solve the following inequality:
how to find the multiplicative inverse of 2-3i
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 a =cosA+isinA,find the value of (1+a)/(1-a)
PROVE THAT A REAL VALUE OF x WILL SATISFY THE EQUATION 1 - ix / 1 + ix = a - ib , if a2 + b2 =1 ; where 'a' and 'b' are real.
Find the square root of this complex number:
2+3i/5-4i + 2-3i/5+4i
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)x2 - (5 -i)x + 2(1-i) = 0
find the square root of
If x is Real , Then (x2 - x + c) / (x2 + 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 (1+i/1-i)3 - (1-i/1+i)3 = x+iy, then find (x,y)
for what values of p does the vertex of the parabola y=x2+ 2px+13 lies at a distance of 5 from the origin
Q. the value of 'b' for which equations
have one root in common is ??
if a+ib =( (x+i)2) / (2x2 + 1)
prove that a2 +b2 =((x2 + 1)2) / (2x2 +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 x2-2ax+a2+a-3 =0 are less than 3 then find the set of all possible values of a. (ans : -infinity, 2)
Find the value of x4 + 4x3 + 6x2 + 4x + 9, when x = -1 + i.sq root of 2
If a+ib = c+i / c-i, where c is real, prove that a2 + b2 =1 and b/a = 2c / c2 -1.
If iZ3+ Z2 - Z + i = 0 ' then show that mode of Z = 1
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