The area of the triangle with vertices P ( z ) , Q ( i z ) and R ( z + i z ) is

Question

TestHub · Accepted Answer

From the above diagram, it is clear that $z, i z$ are perpendicular to each other.

Here, base $= |z|$ , height $= |i z|$

So, area of the triangle formed by the vertices i.e.,

$A = \frac{1}{2} \times base \times height$

$\Rightarrow A = \frac{1}{2} \times |z| \times |i z|$

$\Rightarrow A = \frac{1}{2} {|z|}^{2}$

Hence, the required area is $\frac{1}{2} {|z|}^{2}$ .

Mathematics - Complex Number Question with Solution | TestHub