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`

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=[[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 vec a=( hat i+ hat j+ hat k), vec adot vec b=1a n d vec axx vec b= hat j- hat k ,t h e n hat b is hat i- hat j+ hat k b. 2 hat j- hat k c. hat i d. -i+ 2 hat i

If a^2+b^2+c^2=1,t h e na b+b c+c a lie in the interval [1/3,2] b. [-1,2] c. [-1/2,1] d. [-1,1/2,]

If 1/(b-a)+1/(b-c)=1/a+1/c , then A. a ,b ,a n dc are in H.P. B. a ,b ,a n dc are in A.P. C. b=a+c D. 3a=b+c

The sum of i-2-3i+4 up to 100 terms, where i=sqrt(-1) is a. 50(1-i) b. 25 i c. 25(1+i) d. 100(1-i)

((1 - i)/(1+ i))^(100) = a + ib then (a,b) is ……….

If sin^(-1)((2a)/(1+a^2))+sin^(-1)((2b)/(1+b^2))=2tan^(-1)x , then x is equal to [a , b , in (0,1)] (a) (a-b)/(1+a b) (b) b/(1+a b) (c) b/(1+a b) (d) (a+b)/(1-a b)

If A=[i-i-i i]a n dB=[1-1-1 1],t h e nA^8 equals 4B b. 128 B c. -128 B d. -64 B

Show that a real value of x will satisfy the equation (1-i x)//(1+i x)=a-i b if a^2+b^2=1,w h e r ea ,b real.