IIT JEE , AIEEE Forum - Mathematics , Algebra

sarvpriye

1.)

Let z₁&z₂be any two arbitrary complex nos, then prove that :

| z₁+ z₂| >= 1/2(|z₁| +|z₂|) | z₁/|z₁| + z₂/|z₂| |

2.)

If sin log (iⁱ) = a +ib. find a and b. Hence find cos(log iⁱ).

Ans. a= -1, b= 0, 0

KAB

2)WE know i=cis(pi/2)=e^i(pi/2)

logiⁱ=ilogi=ilog(e^i(pi/2))=i²(pi/2)= - pi/2

So sin(logiⁱ)=sin(-pi/2)= -1= -1+0

So a= -1 b=0

Also cos(logiⁱ)=cos(-pi/2)=0

Hope u r clear!!!

Moderator

Dear Sarvpriye,

Experts answer only one question at a time. Please let us know which of these questions you want to be answered first and then post other queries on a new page

~ forum moderator

Moderator

No response from the post owner, removing question from the pending queue.

~ moderator

Ask & Discuss Questions with Community & Experts