Question

I need some clarification on a problem I am working on. The problem is: Find the real root of square root -1.21. If I am understanding it correctly, square root -1 = i, which is an imaginary number. The number I am trying to find a real root for is square root -1.21.1.1 * 1.1 = 1.21. So, would the real root of square root -1.21 be 1.1i?

Answer 1

Given

$\sqrt[]{-1.21}$$\text{ Use }i^2=-1\text{ and }1.1^2=1.21.$

$\sqrt[]{-1.21}=\sqrt[]{i^2(1.1)^2}=i1.1$

We get the complex number

$i1.1$

This number can be written as follows.

$0+i1.1$

The real part of the complex number is 0 and the imaginary part is 1.1.

There is no real number solution for the given expression.

$\sqrt[]{-1.21}=0+i1.1$