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If z2 = -3 ...

Question

If $z^{2} = - 3 + 4 i$ , then is it true that $z = \pm (1 + 2 i)$ ?

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Solution

$z^{2} = - 3 + 4 i = - 4 + 1 + 4 i = (2 i)^{2} + 1 + 2 * 2 i * 1 = (1 + 2 i)^{2}$

Hence, $z = \sqrt{(1 + 2 i)^{2}} = \pm (1 + 2 i)$

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z_{1} = 1 + 2 i, z_{2} = 2 + 3 i, z_{3} = 3 + 4 i

z_{1}, z_{2}

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z_{2} = - 3 - 4 i

then the equation

| z - z_{1} | + | z - z_{2} | = 10

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z_{1} = 1 + 2 i, z_{2} = 2 + 3 i, z_{3} = 3 + 4 i,

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Type 1 for true and 0 for false

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