There should be no ± in the solution as the question uses radical symbols and as such refers only to the principal roots. √i + √(-i) = {(√2 + i√2) + (√2 - i√2)}/2 = √2.
Yes. If you are going to include non-principal roots, there would be 4 total answers. +/-sqrt(2) and +/-sqrt(2)i. But unless specified, it is just the principle, so just sqrt(2).
The result in the video is not quite correct. Answer (all roots): 𝓍 ∈ { √𝟸,﹣√𝟸, √𝟸 𝒊,﹣√𝟸 𝒊 } Answer (only the principal root): 𝓍 ﹦ √𝟸 I personally think that square roots of complex number constants do not only refer to the principal root, since so many people calculate all roots. But that is debatable. So the video was half-right in either case.
There should be no ± in the solution as the question uses radical symbols and as such refers only to the principal roots. √i + √(-i) = {(√2 + i√2) + (√2 - i√2)}/2 = √2.
Yes. If you are going to include non-principal roots, there would be 4 total answers. +/-sqrt(2) and +/-sqrt(2)i. But unless specified, it is just the principle, so just sqrt(2).
Draw a picture!!!! This is simple geometry. sqrt(i) = (1+i)/sqrt(2). Similarly, sqrt(-i)=(1-i)/sqrt(2). Add them up and
you get sqrt(2). Big deal!
I just wrote i and -i in exponential form. Then raised both to power 1/2. then converted both to sin/cos form.
Could you please lower the volume of the music?
(x ➖ 1ix+1i )
The result in the video is not quite correct.
Answer (all roots):
𝓍 ∈ { √𝟸,﹣√𝟸, √𝟸 𝒊,﹣√𝟸 𝒊 }
Answer (only the principal root):
𝓍 ﹦ √𝟸
I personally think that square roots of complex number constants do not only refer to the principal root, since so many people calculate all roots. But that is debatable. So the video was half-right in either case.