Find the square root of $- 7 - 24 i$

\pm (4 - 3 i)

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\pm (3 + 4 i)

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\pm (3 - 4 i)

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\pm (4 + 3 i)

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Solution

The correct option is C $\pm (3 - 4 i)$
$- 7 - 24 i$
$= 9 - 16 - 2 (3.4) i$
$= 3^{2} + (4 i)^{2} - 2 (3.4 i)$
$= (3 - 4 i)^{2}$
Applying underoot, we get
$\pm (3 - 4 i)$

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Similar questions

∣ ∣ ∣ ∣ ∣ ∣ ∣ \begin{matrix} - 7 & 5 + 3 i & \frac{2}{3} - 4 i 5 - 3 i & 8 & 4 + 5 i \frac{2}{3} + 4 i & 4 - 5 i & 9 \end{matrix} ∣ ∣ ∣ ∣ ∣ ∣ ∣

⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} - 7 & 5 + 3 i & \frac{2}{3} - 4 i 5 - 3 i & 8 & 4 + 5 i \frac{2}{3} + 4 i & 4 - 5 i & 9 \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦

A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 2 - 3 i & 3 + 4 i 2 + 3 i & 0 & 4 - 5 i 3 - 4 i & 4 + 5 i & 2 \end{matrix} ⎤ ⎥ ⎦

7 + 4 i > 5 + 3 i,

i = \sqrt{- 1}

\frac{(3 + 4 i) (4 + 5 i)}{(4 + 3 i) (6 + 7 i)}

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