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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.(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)

^{2}+ y^{2}= (a^{2}+ b^{2}/ c^{2}+ d^{2})a+ibc+id

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

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}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}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 cos theta =(root3 - 1)/(2 root 2) and sin theta =(root3+1)/(2 root 2), then what is the arguement

find sqrt(1-i)

If z = x+iy and w = 1 - i

^{2}/ z-iShow that mod w = 1 implies z is purely real.

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

^{2}+b^{2}=1If 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})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 number_{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 x and y if (1+i)x-2i/3+i + (2-3i)y+i/3-i =i

Find the modulus and argument of complex number z=(1+i)^13/(1-i) ^7

(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}+d2_{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}|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)

If (x + iy) = sqrt [(1+i)/(1-i)],

prove that : x

^{2}+ y^{2}= 1Solve :-

x^{2}-(7 - i) x + (18 - i) = 0 over C.ANURAG.If |a+ib| = 1 then show that 1+b + ai / 1+b-ai = b+ai

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.^{29 }+ 1/i^{29}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.pls solve this question.... if (1+2i)(2+3i)(3+4i)= x+iy.Show that x^2 +y^2 =1625.

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

convert into polar form: sin 50+i cos 50

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.^{2}+|z-z2|^{2}=k will represent a circle if |z1-z2|^{2}<=2kFor 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

If alpha, beta are the roots of ax

^{2}+bx+c=0, find the values of:i. (aplha/beta - beta/alpha)

^{2}ii. alpha

^{3}/beta + beta^{3}/alpha^{24}+(1/i)^{26}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.

Evaluate :

2x

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

^{2}+ x+ 1=0 then find the value ofsummation

_{r=1}^{27}(x^{r}+ 1/x^{r})^{2 }.^{ }if a =cosA+isinA,find the value of (1+a)/(1-a)

If x = cos alpha + i sin alpha, y = cos beta +i sin beta, z = cos gama + i sin gama and if x + y + z = 0, then prove that 1/x + 1/y + 1/z = 0.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.Experts please dont give links and answer with detailed steps

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) = 0Q1. If z

_{1}, z_{2}are the non zero complex root of z^{2}– ax + b = 0 such that |z_{1}| =|z_{2}|, where a, b are complex numbers. If A(z_{1}) , B(z_{2}) and $\angle $AOB = $\mathrm{\theta}$,'O' being the origin, then prove that a^{2}– 4b cos^{2}$\frac{\mathrm{\theta}}{2}$find the square root of

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

If (1+i/1-i)

^{3}- (1-i/1+i)^{3}= x+iy, then find (x,y)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

. the value of 'b' for which equationsQx

^{2}+bx-1=0x

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

${P}{r}{o}{b}{l}{e}{m}{}{2}{}{:}{}{T}{h}{e}{}{l}{a}{r}{g}{e}{s}{t}{}{n}{e}{g}{a}{t}{i}{v}{e}{}{i}{n}{t}{e}{g}{e}{r}{}{w}{h}{i}{c}{h}{}{s}{a}{t}{i}{s}{f}{i}{e}{s}{}\frac{{x}^{2}-1}{\left(x-2\right)\left(x-3\right)}{}{}{}{0}{}{i}{s}{}\phantom{\rule{0ex}{0ex}}\left(A\right){}{-}{4}\left(B\right)-3\phantom{\rule{0ex}{0ex}}\left(C\right)-1\left(D\right)-2\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}{S}{o}{l}{u}{t}{i}{o}{n}{}{:}Bywavycurvemethod$

if a+ib =( (x+i)

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

^{2}=((x^{2}+ 1)^{2}) / (2x^{2}+1)^{2}Find Re(z1z2)

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)(2+i root of 3)

^{2}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.(i) 3-i

^{7}(ii) 5i

^{11}+7i^{3}(iii) 5i

^{-7}+6(iv) 3i

^{-12}+ 8i^{-5}If iZ

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