Question

Find the square roots of the complex number 3+4i

Answer 1

Answer:

❤ANSWER ❤

Strategy: write down an equation satisfied by the square root, and solve it algebraically. Method: square root x+iy satisfies (x+iy)2 = 3 + 4i. Expand: x2-y2 +2xyi = 3+4i.

Step-by-step explanation:

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Answer 2

Answer:

Let

3+4i

=

x

+i

y

Then (

3+4i

)

2

=(

x

+i

y

)

2

⇒3+4i=x−y+2i

xy

Comparing real part and imaginary part, we get

3=x−y and 2

xy

=4⇒xy=4

∴x+y=±5 ( As x



=−5;

x

is real part )

∴x=4,y=1⇒

x

=±2,y=±1

Hence square root is ±(2+i)

Step-by-step explanation:

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