How do I find the square roots of i?

Jamya Elliott

Jamya Elliott

Answered

2022-01-31

How do I find the square roots of i?

Answer & Explanation

Jordyn Horne

Jordyn Horne

Expert

2022-02-01Added 16 answers

Step 1
Let z=reithere be the square-roots of i.
z2=ir2ei(2θ)=ei(π2+2nπ)
{r2=1r=12θ=π2+2nπθ=π4+nπ
z={eiπ4, ei5π4}
={cos(π4)+isin(π4), cos(5π4)+isin(5π4)}
={12+12i, 1212i}

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