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.

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 ???

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 sqrt(1-i)

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 .

if (x+iy)³ = u+iv, then show that u/x +v/y = 4(x² - y²)

find the value of x and y if (1+i)x-2i/3+i + (2-3i)y+i/3-i =i

 if z is a complex number and |z|=1 then prove that z-1/z+1 is a purely imaginary number

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

prove that(x²+y²)²= a²+b²/c²+d2

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?

Solve :- 2x² - (3+7i) x - (3-9i) = 0

ANURAG.

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

Solve :- x² -(7 - i) x + (18 - i) = 0 over C.

ANURAG.

If x + iy = a + ib/a- ib, show that x²+y²=1

If x = 2 + 2^2/3+ 2^1/3, 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 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 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 a_n=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

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 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

how to find the multiplicative inverse of 2-3i

express 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.

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.

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

1. 5+12i
2. -4-3i

Q. the value of 'b' for which equations

x²+bx-1=0

x²+x+b=0

have 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) / (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)

If a+ib = c+i / c-i, where c is real, prove that a² + b² =1 and b/a = 2c / c² -1.