Question

if z square = 3-4i, then z=......​

Answer 1

Answer:

root of 3-4i

......

......

Answer 2

Answer:

Solve: Z2 = 3 - 4i

Let

z= x + yi

Rewrite as

(x + yi)2 = 3 - 4i

Expand

x2 +2xyi + y2i2 = 3 - 4i

Simplify

x2 - y2 + 2xyi = 3 - 4i

real/imag parts

x2 - y2 = 3

and

2xy = -4

xy = -2

Therefore y = -2/x

Substitute

y = -2/x into x2 - y2 = 3

giving

x^2 - 4/x2 = 3

Multiply by x2

x^4 - 4 = 3x^2

Factor

Roots **>

x^4 - 3x^2 - 4 = 0

(x2 + 1) (x2 - 4) = 0

(x2 + 1) (x + 2) (x - 2) = 0

Given xy = -2

for x = 2 then y = -1 therefore z = 2 - i

for x = -2 then y = 1 therefore z = -2 + i

OK... the 2 solutions for z shown are indicated as correct in the text, but these are the onnly solutions given.