Finding the Square Roots of a Complex Number In Exercises 31–38, find the square roots of the complex number.

Cheyanne Leigh

Cheyanne Leigh

Answered question

2021-09-07

Finding the Square Roots of a Complex Number In Exercises 31–38, find the square roots of the complex number.
31. 2i

Answer & Explanation

grbavit

grbavit

Skilled2021-09-08Added 109 answers

31. Given,
z=2i
z=0+2i
Now comparing with z=x+yi, we get
x=0andy=2
Now,
r=x2+y2
=02+22
=2
and
θ=tan1(yx)
=tan1(20)
=tan1()
=π2
Now polar form is,
z=r(cosθ+isinθ)
z=2(cosπ2+isinπ2)
Step 2
Now square root is,
z=2i
=2(cosπ2+isinπ2)
=2[cosπ2+isinπ2]12
=±(2)12(cos(12π2)+isin(12π2))
[(cosθ+isinθ)n=cos(nθ)+isin(nθ)]
=±2(cos(π4)+isin(π4))
=±2(12+i12)
=±(1+i)

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