Engineering Board Exam Reviewer · Complex Numbers: Operations · medium

Find the square roots of 3+4i.

1. (2-i)
2. (1+2i)
3. ≤ft( 32+2i )
4. (2+i)

Answer

D. (2+i)

Solution

Let (a+bi)2=3+4i: a2-b2=3 and 2ab=4. Then b=2/a and a4-3a2-4=0 a2=4, a= 2, b= 1. So the roots are (2+i).

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1. Simplify 1i+ 11+i.
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3. Find the roots of z2+2z+5=0.
4. Find the modulus of (3+4i)(5-12i).
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