How do you express $9isqrt(-36)$ as a product of a real number and i?

Question

2378 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-11-05T13:20:45

$9isqrt(-36)=-54$

First of all, we need to get rid of the square root: since $sqrt(a*b)=sqrt(a)sqrt(b)$ , we have that $sqrt(-36)=sqrt(-1)sqrt(36) = i * 6$ .

So, the whole expression becomes

$9i * 6i = 54 i^2 = -54$ , so it was actually a real number, and you can't write it as a product of a real number and i

How do you express 9isqrt(-36)9isqrt(-36) as a product of a real number and i?