Question

If the area of the triangle formed by the vertices z, iz and z+iz is 50 square units, then find the value of |z|

Answer 1

Answer:

the value of |z| = 10

Step-by-step explanation:

If the area of the triangle formed by the vertices z, iz and z+iz is 50 square units, then find the value of |z|

Length of three sides

z & iz  = √(z-0)² + (0-z)² = |z|√2

z & z + iz = √(z-z)² + (0-z)² = |z|

iz & z + iz = √(0-z)² + (z-z)² = |z|

are |z|√2  , |z|  & |z|

s =  (|z| +  |z| +  |z|√2)/2

s = |z| +  |z|/√2

Area of triangle  using hero formula

=√( |z| +  |z|/√2)( |z| +  |z|/√2 -z)( |z| +  |z|/√2 -z)( |z| +  |z|/√2 -  |z|√2)

=√( |z| +  |z|/√2)( |z|/√2)( |z|/√2)( |z| -  |z|/√2)

= √(|z|² - |z|²/2)(|z|²/2)

= √(|z|²/2)(|z|²/2)

=|z|²/2

Area of triangle = 50 sq units

|z|²/2 = 50

=> |z|² = 100

=> |z| = 10

the value of |z| = 10