Set of complex numbers with a property

Algebra Level pending

let $A=\{a+ib \big|a,b \in Z\}$ . Here $i=\sqrt{-1}$ is a imaginary unit. $U=\{x\in A \big| \frac{1}{x} \in A\}$ . find the number of elements in $U$ .

The answer is 4.

1 solution

A Former Brilliant Member
May 13, 2020

let $x=a+bi$ be a complex number $\frac{1}{x}=\frac{1}{a+ib} = \frac{a-ib}{a^{2}+b^{2}}$ , now denominator is equal to one and $a\in Z$ and $b\in Z$ is the sufficient and necessary condition for this question. the solutions are $\big(a,b\big)$ $\in$ $\{\big(0,1\big),\big(1,0\big),\big(-1,0\big),\big(0,-1\big)\}$ there are only four solutions.

You should write $a,b\in Z$ in the question.

Shikhar Srivastava - 1 year, 1 month ago

thank you . I changed it

A Former Brilliant Member - 1 year, 1 month ago

Set of complex numbers with a property

The answer is 4.

1 solution

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