Question

Separate the real and imaginary parts of (-1+√-2)²​

Answer 1

Answer:

real part = -1 , imaginary part = -2√2 i

Step-by-step explanation:

to identify them, let us simplify (-1+√-2)²,

(-1+√-2)² = (-1)²+(√-2)² + 2(-1)(√-2)

= 1+(-2) -2√-2

= -1 -2√-2

√-2 can be written as √2 i. here i is imaginary number which is equal to √-1

so, (-1+√-2)² = -1-2√2 i

so, real part = -1 , imaginary part = -2√2 i

Answer 2

Answer:

$\text{ Real part=} -1 \text{ and imaginary part=}-2\sqrt2i$

Step-by-step explanation:

$(-1+\sqrt{-2})^2 = (-1+\sqrt{2} i)^2 \\\\=1+2i^2 - 2\sqrt2 i\\\\=1-2-2\sqrt2i \text{ (as } i^2=-1)\\\\=-1-2\sqrt2i\\\\So ,\text{ Real part=} -1 \text{ and imaginary part=}-2\sqrt2i$