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Algebra

New kid on the Block

 Joined: 10 Aug 2012 Post: 1
10 Aug 2012 11:36:28 IST
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Engineering Entrance , JEE Main , JEE Advanced , Mathematics , Algebra

if the area of the triangle formed by z,iz,z+iz is 30 then find the |z|.

Cool goIITian

Joined: 21 Apr 2012
Posts: 75
10 Aug 2012 14:28:36 IST
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According to the Herons formula

s= z + iz + z+ iz = 2z + 2iz = 2z(1+ i)

now area of triangle = square root of (s)(s+a)(s+b)(s+c)

put  s value and you will get the answer of z.

Blazing goIITian

Joined: 1 Apr 2007
Posts: 4025
11 Aug 2012 16:12:31 IST
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if you draw a graph between real and imaginary z

you get three points z,z+iz,iz

it forms a right angled traingle

so its area is 1/2*base*height

bASe is mod( z)

height ismod( z)

so area is 1/2*mod( z)*mod( z)=30

so mod( z)=sqrt(60)

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