A number of the form a + ib is called a complex number, where `a,b in R and i=sqrt(-1)` Complex number is usually denoted by Z and the set of complex number is represented by C. Thus `C={a+ib:a,b inB and -=sqrt(-1)}.If Z =a+ib` is a complex number then `bar(z)a=-ib` is called as conjugate. Two complex numbers `z1=a1+ib_(1)&z2=a2+ib2` are equal if and only if their real and imaginary parts are equal respectively. i.e., `z_(1)=z_(2)hArrRe(z_(1))=Re(z_2)and Im(z_1)=Im (z_(2))hArra_(1)=a_(2)and b_(1)=b_(2).` The following algebric operations can be performd on complex numbers.
`{:(1.,"Addition",(a+bi)+(c+bi)=a+bi+c+di=(a+c)+(b+d)i),(2.,"Subtraction",(a+b)-(c+di)=a+bi-c-di=(a-c)+(b-d)i),(3.,"Multipication",(a+b)(c+di)=ac+adl+bci+bdi2=(ac-bd)+(ad+bc)i),(4.,"Multiplication",(a+bi)/(c+di)=(a+di)/(c+di).(c-di)/(c-di)=(ac+bd)/(c^(2)+d^(2))+(bc-ad)/(c^(2)+d^(2))i):}`
Using above comprehension answer the followings :
If `a^(2)+b^(2)=1.Then(1+b+ia)/(1+b-ia)=`

A number of the form a + ib is called a complex number, where a,b in R and i=sqrt(-1) Complex number is usually denoted by Z and the set of complex number is represented by C. Thus C={a+ib:a,b inB and -=sqrt(-1)}.If Z =a+ib is a complex number then bar(z)a=-ib is called as conjugate. Two complex numbers z1=a1+ib_(1)&z2=a2+ib2 are equal if and only if their real and imaginary parts are equal respectively. i.e., z_(1)=z_(2)hArrRe(z_(1))=Re(z_2)and Im(z_1)=Im (z_(2))hArra_(1)=a_(2)and b_(1)=b_(2). The following algebric operations can be performd on complex numbers. {:(1.,"Addition",(a+bi)+(c+bi)=a+bi+c+di=(a+c)+(b+d)i),(2.,"Subtraction",(a+b)-(c+di)=a+bi-c-di=(a-c)+(b-d)i),(3.,"Multipication",(a+b)(c+di)=ac+adl+bci+bdi2=(ac-bd)+(ad+bc)i),(4.,"Multiplication",(a+bi)/(c+di)=(a+di)/(c+di).(c-di)/(c-di)=(ac+bd)/(c^(2)+d^(2))+(bc-ad)/(c^(2)+d^(2))i):} Using above comprehension answer the followings : If (x^(2)+x)+iyand(-x-1)-i(x+2y) are conjugate of each other, then real value of x y are

A number of the form a + ib is called a complex number, where a,b in R and i=sqrt(-1) Complex number is usually denoted by Z and the set of complex number is represented by C. Thus C={a+ib:a,b inB and -=sqrt(-1)}.If Z =a+ib is a complex number then bar(z)a=-ib is called as conjugate. Two complex numbers z1=a1+ib_(1)&z2=a2+ib2 are equal if and only if their real and imaginary parts are equal respectively. i.e., z_(1)=z_(2)hArrRe(z_(1))=Re(z_2)and Im(z_1)=Im (z_(2))hArra_(1)=a_(2)and b_(1)=b_(2). The following algebric operations can be performd on complex numbers. {:(1.,"Addition",(a+bi)+(c+bi)=a+bi+c+di=(a+c)+(b+d)i),(2.,"Subtraction",(a+b)-(c+di)=a+bi-c-di=(a-c)+(b-d)i),(3.,"Multipication",(a+b)(c+di)=ac+adl+bci+bdi2=(ac-bd)+(ad+bc)i),(4.,"Multiplication",(a+bi)/(c+di)=(a+di)/(c+di).(c-di)/(c-di)=(ac+bd)/(c^(2)+d^(2))+(bc-ad)/(c^(2)+d^(2))i):} Using above comprehension answer the followings : If (x^(2)+x)+iyand(-x-1)-i(x+2y) are conjugate of each other, then real value of x y are

If z = a+ib is a complex numbers, then

If z = a+ib is a complex numbers, then

The conjugate of the complex number (a+ib) is :

The conjugate of the complex number (a+ib) is :

The modulus of the complex number z =a +ib is

The modulus of the complex number z =a +ib is

Express of the complex number in the form a+ib .

Express of the complex number in the form a+ib .