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

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Solution

Let $Z = 3 + 4 z ∴ Z - 3 = 4 z$
$∴ {| Z - 3 |}^{2} = 16 {| z |}^{2} = 32 = {(4 \sqrt{2})}^{2}$
$∴ Z$ clearly lies on a circle whose center is $(3, 0)$ and radius $4 \sqrt{2}$ .

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If |z|=√2, then the points given by 3+4z will lie on a circle. What is the centre and radius of this circle?

Let Z=3+4z∴Z−3=4z∴|Z−3|2=16|z|2=32=(4√2)2∴Z clearly lies on a circle whose center is (3,0) and radius 4√2.

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

Let $Z = 3 + 4 z ∴ Z - 3 = 4 z$
$∴ {| Z - 3 |}^{2} = 16 {| z |}^{2} = 32 = {(4 \sqrt{2})}^{2}$
$∴ Z$ clearly lies on a circle whose center is $(3, 0)$ and radius $4 \sqrt{2}$ .