If i=-1, then 4+5-12+i32334+3-12+i32365 is equal to
1-i-3
-1+i-3
i3
-i3
1+i3
Explanation for correct option:
Given: i=-1and 4+5-12+i32334+3-12+i32365
If in a complex number a+ib, the ratio of a:b=1:3, then it always convert the complex number in ω
∴-12+i32=ω
So, 4+5-12+i32334+3-12+i32365=4+5ω334+3ω365
=4+5ω333(ω)+3ω363(ω2)=4+5(ω)3111(ω)+3(ω)3121(ω2)=4+51111(ω)+31121(ω2)[∵ω3=1]=1+3+3(ω)+2(ω)+3(ω2)=1+2(ω)+3(1+ω+ω2)=1+2(ω)+0[∵1+ω+ω2=0]=1+2-12+i32=1-1+i3
⇒ 4+5-12+i32334+3-12+i32=i3
Hence option(C) is correct.
Write = or ≠ in the place holder.18□34
Consider two events A and B such that P(A)=14, P(BA)=12, P(AB)=14. For each of the following statements, which is true.
I.P(A'B')=34
II. The events A and B are mutually exclusive
III.P(AB)+P(AB')=1