SOLUTION: Find real numbers a and b such that (𝑎 + 𝑏i)^2 = −3 − 4i

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Question 1162768: Find real numbers a and b such that (𝑎 + 𝑏i)^2
= −3 − 4i
Answer by Alan3354(69443) About Me  (Show Source):
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Find real numbers a and b such that (𝑎 + 𝑏i)^2
= −3 − 4i
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a^2 + 2abi - b^2 = -3 - 4i
a^2 - b^2 = -3
2ab = -4
-----------
b^2 - a^2 = 3
b = -2/a
---
4/a^2 - a^2 = 3
4 - a^4 = 3a^2
a^4 + 3a^2 - 4 = 0
(a^2 + 4)*(a^2 - 1) = 0
a = 1
b = -2
---
Check:
(1 - 2i)*(1 - 2i) = 1 -4 - 4i = -3 - 4i
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a = -1
b = 2
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