Find the square root of 4-3i?

2 Answers

z = pm (3 - i)/2 sqrt 2

Explanation:

z^2 = 4 - 3i = (x + yi)^2 = x^2 - y^2 + 2xyi

x^2 - y^2 = 4
2xy = -3 => y = -3/(2x)

x^2 - 9/(4x^2) = 4, x^2 = a

4a^2 - 16a - 9 = 0

Delta = 256 + 4 * 4 * 9 = 400

x^2 = (16 pm 20)/8 > 0

x = pm 3/sqrt2 = pm 3/2 sqrt 2

y = -pm3/2 * sqrt 2/3 = - pm 1/2 sqrt 2

Aug 8, 2018

4-3i

=1/2(8-2.3*i)

=1/2(3^2+i^2-2.3*i)

=1/2(3-i)^2

Square root of 4-3i

pm1/sqrt2(3-i)