Finding Square Roots of Complex Numbers

Dr. Aruna Kulkarni explains the process of finding the square root of a complex number using equations for real and imaginary parts. By solving the equations step by step, the square roots of the complex number are determined. The final result is presented, showcasing the values of a and b in the complex number.

• Complex numbers
• Square root
• Equations
• Dr. Aruna Kulkarni
• Mathematics

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Uploaded on Sep 12, 2024 | 0 Views

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1. To find the Square Root of a Complex Number Dr. Aruna Kulkarni

2. ???? ?? ????? 7 + 24? Solution: Let 7 + 24? = ? + ?? .a, b ? 7 + 24? = ? + ??2 7 + 24? = ?2+2??? + ?2?2 7 + 24? = (?2 ?2)+2abi Equating real and imaginary parts, we get

3. (?2?2)= 7 .. .. I and 2ab = 24 . II b= 24/2a=12/a ?2 ? ?2 144 ?4 144 ?2 2=7 ..from I 12 ?2=7 = 7 ?4 144 = 7?2

4. ?4 7?2 144 = 0 (?2 16)(?2+9) = 0 (?2 16) = 0 ??(?2+9) = 0 ?2= 16 ?? ?2= 9 ??? ?2 9 as a R ?2=16 ? = 4

5. When a= 4, b=12 a= -4, b=12 4 =3 4= -3 7 + 24? = 4 + 3? Thank You