Question

find thesquare root of 2-2i​

Answer 1

Answer:

Let, √(2 - 2i) = a + bi

On squaring,

» 2 - 2i = a² - b² + 2abi

On comparing real and imaginary parts we get

» a² - b² = 2 ... (1) & ab = - 1 ... (2)

» b = -1/a

» a² - (-1/a)² = 2

» a² - 1/a² = 2

» a⁴ - 2a² - 1 = 0

» a² = (2 ± √8)/2

» a = ±√(1 + √2)

» b = -1/a

» b = -1/[±√(1 + √2)]

» b = -[√(1 + √2)] / (1 + √2) = -√(1 + √2)

= [√(1 + √2)] / (1 + √2) = √(1 + √2)

Therefore, a + bi = { √(1 + √2) - √(1 + √2)i } or

a + bi = { -√(1 + √2) + √(1 + √2)i }.

Answer 2

Answer:

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