If `z(1+a)=b+i ca n da^2+b^2+c^2=1,` then `[(1+i z)//(1-i z)=`
A. `(a+i b)/(1+c)`
B. `(b-i c)/(1+a)`
C. `(a+i c)/(1+b)`
D. none of these

If a^2+b^2=1 t h e n (1+b+i a)/(1+b-i a)= 1 b. 2 c. b+i a d. a+i b

Find z^(-1) , if z = ( 2 +3i)(1-i)

If A^3=O ,t h e nI+A+A^2 equals a. I-A b. (I+A^1)^(-1) c. (I-A)^(-1) d. none of these

Given z=f(x)+ig(x)w h e r ef,g:(0,1)to(0,1) are real valued functions. Then which of the following does not hold good? z=1/(1-i x)+i1/(1+i x) b. z=1/(1+i x)+i1/(1-i x) c. z=1/(1+i x)+i1/(1+i x) d. z=1/(1-i x)+i1/(1-i x)

If z_(1) =2 -i, z_(2)=1+i , find |(z_(1) + z_(2) + 1)/(z_(1)-z_(2) + 1)|

If z_(1) = 2 - i and z_(2) = -4 + 3i, find the inverse of z_(1)z_(2) and (z_(1))/(z_(2)) .

If A=[[a+i b, c+i d],[-c+i d, a-i b]]a n da^2+b^2+c^2+d^2=1,t h e nA^(-1) is equal to a. [[a+i b,-c+i d],[-c+i d, a-i b]] b. [[a-i b,-c-i d],[-c-i d, a+i b]] c. [[a+i b,-c-i d],[-c+i d, a-i b]] d. none of these

If Z is an idempotent matrix, then (I+Z)^n I+2^n Z b. I+(2^n-1)Z c. I-(2^n-1)Z d. none of these

If z_(1)=2-i, z_(2)=1+i , find |(z_(1)+z_(2)+1)/(z_(1)-z_(2)+1)| .