A problem from complex number chapter

Algebra Level 3

∣ 3 + i ∣ x = 2 x \large \left|\sqrt 3 +i \right|^x =2^x

What is the number of non-zero integral solution to the equation above?

Notations:

2 Infinitly many 1 0

Nitesh Chaurasia by Nitesh Chaurasia , 23, Nepal

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Chew-Seong Cheong
Aug 28, 2017

∣ 3 + i ∣ x = 2 x ( ( 3 ) 2 + 1 2 ) x = 2 x 2 x ≡ 2 x \begin{aligned} \left|\sqrt 3 + i \right|^x & = 2^x \\ \left(\sqrt{(\sqrt 3)^2 + 1^2}\right)^x & = 2^x \\ 2^x & \equiv 2^x \end{aligned} .

Since the LHS is identical to the RHS, there are infinitely many non-negative integral solutions to the equation.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Can you plz tell me how did you convert the mod in square root?

Utkarsh Kumar - 3 years, 9 months ago

Log in to reply

∣ a + i b ∣ = a 2 + b 2 |a+ib| = \sqrt{a^2+b^2} .

Chew-Seong Cheong - 3 years, 9 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...