how can I simplify this $\sqrt{i}+\sqrt{2i}+\sqrt{3i}$

Question

Is there an easy way to simplify the $$\sqrt{i}+\sqrt{2i}+\sqrt{3i}$$

what's your definition of $\sqrt{i}$? But either way, $\sqrt{i} + \sqrt{2i} + \sqrt{3i} = (1+ \sqrt{2}+\sqrt{3}) \sqrt{i}$ — Tryss, Apr 18 '15 at 18:31

score 5 · Accepted Answer · answered Apr 18 '15 at 18:33

5

HINT: write $i=e^{i\frac{\pi}{2}}$ and everything should follow.

answered Apr 18 '15 at 18:33

QuantumEyedea

2,805

E.H.E · Answer 2 · 2015-04-18T19:32:31.490

0

you can use the following $$i=\frac{1}{2}(1+i)^2$$ so $$\sqrt{i}=\sqrt{\frac{1}{2}(1+i)^2}=\frac{1}{\sqrt{2}}(1+i)$$ $$\sqrt{2i}=\sqrt{\frac{2}{2}(1+i)^2}=(1+i)$$ $$\sqrt{3i}=\sqrt{\frac{3}{2}(1+i)^2}=\sqrt{\frac{3}{2}}(1+i)$$

edited Apr 18 '15 at 19:32

answered Apr 18 '15 at 18:38

E.H.E

23,280

In complex numbers, we do not have $\sqrt{z^2} = |z|$. – GEdgar Apr 18 '15 at 18:53
1

@Essam consider $\sqrt{(i)^2}$ – Nick Apr 18 '15 at 19:03
@GEdgar thank you for your comment – E.H.E Apr 18 '15 at 19:08

how can I simplify this $\sqrt{i}+\sqrt{2i}+\sqrt{3i}$

2 Answers2