Find the square root of 3-4i by complex method

1.	Find the square root of 3-4i by complex method
Answer» ANSWER: $\sqrt{3-4i}= 2-i\:\:(or)\:\:-2+i$ Step-by-step explanation: Square root of 3 - 4i is found by using algebraic identity. In this METHOD the given COMPLEX NUMBER is MODIFIED as a perfect square by using suitable algebraic identity. Formula used: $(a-b)^2=a^2+b^2-2ab$ Now, $3 - 4i = (4-1) - 4i\\\\3 - 4i = (2^2+i^2) - 22i\\\\3 - 4i = (2 - i)^2\\\\\sqrt{3-4i}= 2-i\:or\:-(2-i)\\\\\sqrt{3-4i}= 2-i\:or\:-2+i$

Answer»

$\sqrt{3-4i}= 2-i\:\:(or)\:\:-2+i$