Question

If $\left|z\right|=\sqrt{2},$ then the points given by 3 +4z will lie on a circle. What is the centre and radius of this circle ?

• A. $\therefore$ Z clearly lies on a circle whose centre is (3,0) and radius $4.$
• B. $\therefore$ Z clearly lies on a circle whose centre is (3,0) and radius $2\sqrt{2}.$
• C. $\therefore$ Z clearly lies on a circle whose centre is (3,0) and radius $4\sqrt{2}.$
• D. $\therefore$ Z clearly lies on a circle whose centre is (2,0) and radius $2\sqrt{2}.$

Answer 1

The correct option is C $\therefore$ Z clearly lies on a circle whose centre is (3,0) and radius $4\sqrt{2}.$

Let $Z=3+4z$

$\therefore Z-3=4z$

$\therefore {|Z-3|}^2=16{\left|z\right|}^2=32={\left(4\sqrt{2}\right)}^2$

$\therefore$ Z clearly lies on a circle whose centre is (3,0) and radius $4\sqrt{2}.$
Ans: C