If \( (a+i b)=\frac{c+i}{c-i} \), where \( c \) is real, prove that \( a^{2}+b^{2}=1 \) and \( \... VIDEO
If \( (a+i b)=\frac{c+i}{c-i} \), where \( c \) is real, prove that \( a^{2}+b^{2}=1 \) and \( \frac{b}{a}=\frac{2 c}{c^{2}-1} \).
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live
Other Videos By PW Solutions 2022-10-26 Find the real values of \( x \) and \( y \) for which: \[ (x+i y)(3-2 i)=(12+5 i) \] 2022-10-26 If \( \left(\frac{1+i}{1-i}\right)^{3}-\left(\frac{1-i}{1+i}\right)^{3}=x+i y \), find \( x \) a... 2022-10-26 If \( a=(\cos \theta+i \sin \theta) \), prove that \( \frac{1+a}{1-a}=\left(\cot \frac{\theta}{2... 2022-10-26 A coil of insulated copper wire is connected to a galvanometer. What would happen, if a strong ba... 2022-10-26 Find the real values of \( x \) and \( y \) for which: \[ x+4 y i=i x+y+3 \] 2022-10-26 A magnetic compass needle is placed in the plane of paper near point A as shown in the figure. In... 2022-10-26 If \( z_{1}=(2-i) \) and \( z_{2}=(1+i) \), find \( \left|\frac{z_{1}+z_{2}+1}{z_{1}-z_{2}+i}\ri... 2022-10-26 Find the real values of \( x \) and \( y \) for which: \[ (1-i) x+(1+i) y=1-3 i \] 2022-10-26 What are magnetic field lines? Justify the following statements.
(i) Two magnetic field lines nev... 2022-10-26 Find the smallest positive integer \( n \) for which \( (1+i)^{2 n}=(1-i)^{2 n} \). 2022-10-26 If \( (a+i b)=\frac{c+i}{c-i} \), where \( c \) is real, prove that \( a^{2}+b^{2}=1 \) and \( \... 2022-10-26 \( \left(2^{3 n}-1\right) \) is a multiple of 7 . 2022-10-26 If \( \left(\frac{1-i}{1+i}\right)^{100}=(a+i b) \), find the values of \( a \) and \( b \). 2022-10-26 State right hand thumb rule to determine the direction of magnetic field around a current carryin... 2022-10-26 Show that \( (1-i)^{n}\left(1-\frac{1}{i}\right)^{n}=2^{n} \) for all \( n \in N \). 2022-10-26 \( 3^{n} \geq 2^{n} \) 2022-10-26 Let \( A=\{-1,0,1,2\} \) and \( B=\{2,3,4,5\} \). Find which of the following are functions from... 2022-10-26 If \( (x+i y)=\frac{a+i b}{a-i b} \), prove that \( x^{2}+y^{2}=1 \). 2022-10-26 The flow of current in a circular wire creates a magnetic field at its centre. How can existence ... 2022-10-26 \( \left(3^{2 n+2}-8 n-9\right) \) is divisible by 8 . 2022-10-26 \( \left(1+\frac{3}{1}\right)\left(1+\frac{5}{4}\right)\left(1+\frac{7}{9}\right) \ldots\left\{1...