Question

Find the conjugate of $Z=\sqrt{3}i+1$

• A. $1-\sqrt{3}i$
• B. $\frac{1}{1+\sqrt{3}i}$
• C. $1$
• D. $\sqrt{3}i$

Answer 1

The correct option is A $1-\sqrt{3}i$

$Z=1+\sqrt{3}i$

and we know that,

$Z.Z_c=|Z{|}^2=(\sqrt{1^2+{\sqrt{3}}^2}{)}^2=2^2=4$

as $(1+\sqrt{3}i)(1-\sqrt{3}i)=1^2-(\sqrt{3}i{)}^2=1-(-3)=1+3=4$

it's conjugate will be $=Z_c=1-\sqrt{3}i$