00:01
In this question it is given that magnitude of z minus iota upon z plus 2 aita equal 1 and magnitude of z equal 5 5 .2 and we have to find the value of z plus 3 aata.
00:15
So first we will assume let z equal x plus iata y.
00:23
Now it is given that magnitude of z minus iata upon z plus 2 aata.
00:32
Equal 1.
00:34
So we can write x plus iata y minus aita upon x plus iata y plus 2 a magnitude equal 1.
00:49
So we can write x plus iata into y minus 1 upon x plus iata into y minus 1 so magnitude of x plus aeta, iata, y minus 1 equal magnitude of x plus iata y plus 2.
01:19
Now we can write under root x square magnitude of x plus iata y minus 1 equal under root x squared plus y minus 1 plus y plus 2 whole square this equal x square plus y minus 1 square equal x square plus y plus 2 whole square this comes out to be x square x square plus y square minus 2 y plus 1 equal x square plus y square plus 4 y plus 4 now minus 2y plus 1 equal 4y plus 4y plus 4.
02:17
So we can write 6y equal minus 3.
02:22
So y equals minus 1 by 2.
02:24
Now it is given that magnitude of z equal 5 by 2.
02:30
So we can write x squared plus y square under root equal 5 by 2.
02:36
So x squared plus y square equal 5 by 2...