Question

find the sqrt of -2i​

Answer 1

Answer:

4

Step-by-step explanation:

(2)2=4

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Answer 2

√-2i

√-2i = a + bi

squaring both the side

-2i = (a + bi)²

-2i = a² + 2abi + b²i²

-2i = a² - b² + 2abi ...i² = -1

-2i = (a² - b²) + 2abi

Equating real and imaginary parts

a² - b² = 0 and -2i = 2abi

a² - b² = 0 ...(1) and ab = -1 •°• b = -1/a ...(2)

substituting in 1

a² - (-1/a)² = 0

a² - 1/a² = 0 •°• (a⁴ - 1)/a² = 0

a⁴ - 1 = 0 •°• a⁴ = 1 •°• a = 1 ....(3)

substituting in 2

b = -1/(1) = -1 •°• b = -1

•°• √2i = a + bi = 1 - i

•°• sqrt of -2i is 1 - i