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Question
If the area of the triangle formed by the vertices z, iz, and z + iz is 50 square units, find the value of |z|
Solution
The given vertices are z, iz, z + iz ⇒ z, iz are ⊥r to each other.
Area of triangle = `1/2` bh = 50
⇒ `1/2 |"z"| |"iz"|` = 50
⇒ `1/2 |"z"| |"z"|` = 50
⇒ |z|2 = 100
⇒ |z| = 10
Aliter:
Given the area of triangle = 50 sq.unit
`1/2 |(x, y, 1),(-x - y, x + y, 1),(-y, x, 1)|` = 50
`{:("R"_2 -> "R"_2 - "R"_3),(->):} 1/2 |(x, y, 1),(0, 0, -1),(-y, x, 1)|` = 50
`1/2 [""^(+1)[(x, y),(-y, x)]]` = 50
`1/2 [x^2 + y^2]` = 50
x² + y² = 100
|z|² = 100
|z| = 10
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