AP EAMCET · Maths · Complex Number
If \(z, i z\) and \(z+i z\) are the vertices of a triangle and if \(|z|=4\), then the area (in sq. units) of that triangle, is
- A \(4\)
- B \(8\)
- C \(16\)
- D \(32\)
Answer & Solution
Correct Answer
(B) \(8\)
Step-by-step Solution
Detailed explanation
Vertices: \(V_1=z\), \(V_2=iz\), \(V_3=z+iz\). Vectors from \(V_3\): \(V_3V_1 = z-(z+iz) = -iz\) and \(V_3V_2 = iz-(z+iz) = -z\). The ratio of these vectors is \(\frac{-iz}{-z} = i\). Since the ratio is purely imaginary, vectors \(V_3V_1\) and \(V_3V_2\) are perpendicular,…
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