Question

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

Answer 1

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,

$3 - 4i = (4-1) - 4i\\\\3 - 4i = (2^2+i^2) - 2*2*i\\\\3 - 4i = (2 - i)^2\\\\\sqrt{3-4i}= 2-i\:or\:-(2-i)\\\\\sqrt{3-4i}= 2-i\:or\:-2+i$