Let \( z_{1}, z_{2}, z_{3} \) are three pair wise distinct complex numbers and \( t_{1}, t_{2}, ... VIDEO
Let \( z_{1}, z_{2}, z_{3} \) are three pair wise distinct complex numbers and \( t_{1}, t_{2}, t_{3} \) are non-negative real numbers such that \( t_{1}+t_{2}+ \) \( t_{3}=1 \). Prove that the complex number \( z=t_{1} z_{1}+t_{2} z_{2}+t_{3} z_{3} \) lies inside a triangle with vertices \( z_{1}, z_{2}, z_{3} \) or on its boundry.https://bit.ly/YTAI_PWAP https://www.pw.live
Other Videos By PW Solutions 2023-07-03 If the line \( y=4+k x, k0 \), is the tangent to the parabola \( y=x-x^{2} \) at the point \( P ... 2023-07-03 If \( y=m_{1} x+c_{1} \) and \( y=m_{2} x+c_{2}, m_{1} \neq m_{2} \) are two common tangents of ... 2023-07-03 Let \( x^{2}+y^{2}+A x+B y+C=0 \) be a circle passing through \( (0,6) \) and touching the parab... 2023-07-03 Let \( S=z \in C:|z-3| \leq 1 \) and \( z(4+3 i)+\bar{z}(4-3 i) \leq 24 \).
If \( \alpha+i \beta... 2023-07-03 On the Argand plane \( z_{1}, z_{2} \) and \( z_{3} \) are respectively the vertices of an isosc... 2023-07-03 Prove that the locus of intersections of tangents to the parabola \( y^{2}=4 a x \) which interc... 2023-07-03 If \( z_{1} \) and \( z_{2} \) are two complex number and if \( \arg \frac{z_{1}+z_{2}}{z_{1}-z_... 2023-07-03 If \( P \) is a point on the Aragand diagram. On the circle with \( O P \) as diameter two point... 2023-07-03 Let \( A \equiv z_{1} ; B \equiv z_{2} ; C \equiv z_{3} \) are three complex numbers denoting th... 2023-07-03 \( z_{1}, z_{2} \) and \( z_{3} \) are three non-zero complex numbers such that \( z_{1} \neq z_... 2023-07-03 Let \( z_{1}, z_{2}, z_{3} \) are three pair wise distinct complex numbers and \( t_{1}, t_{2}, ... 2023-07-03 Given, \( z=\cos \frac{2 \pi}{2 n+1}+i \sin \frac{2 \pi}{2 n+1} \), \( n \) a positive integer... 2023-07-03 Show that all roots of the equation \( a_{0} z^{n}+a_{1} z^{n-1}+\ldots+a_{n-1} z \) \( +a_{n}=n... 2023-07-03 Match the statements in Column-I with those in Column-II [Note: Here \( z \) takes values in the... 2023-07-03 A particle starts to travel from a point \( P \) on the curve \( C_{1} \) : \( |z-3-4 i|=5 \), w... 2023-07-03 \( \omega_{1}, \omega_{2}, \ldots, \omega_{n} \) be complex numbers. A line \( L \) in the argan... 2023-07-03 If \( z_{1}, z_{2}, z_{3} \) be vertices of an isosceles \( \Delta \) right angled at \( z_{3} \... 2023-07-03 If \( \omega \) is the imaginary cube root of unity, then find the number of pairs of integers \... 2023-07-03 If \( z \) is a complex number and the minimum value of \( |z|+|z-1| \) \( +|2 z-3| \) is \( \la... 2023-07-03 If \( \mathrm{z} \in C \), then the locus of \( z \) on an Argand diagram is
\begin{tabular}{|l|... 2023-07-03 If \( \mathrm{z} \in C \), then the locus of \( z \) on an Argand diagram is
\begin{tabular}{|l|...
0