Make complex number to imaginary number.

Algebra Level pending

There is a complex number that ( a + b i ) (a+bi) . I want to square it and make it into an imaginary number. Which of the following must be true?

a < b a < b a ≥ b a \geq b a ≠ b a \neq b a > b a > b a = ± b a = \pm b a ≤ b a \leq b

. . by . . , 14, South Korea

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1 solution

. .
Feb 9, 2021

The answer is a = b a = b because if a = b a = b , then ( a + a i ) 2 = a 2 − a 2 + 2 a 2 i (a + ai)^{2} = a^{2}-a^{2}+2a^{2}i . Then it is equal to 2 a 2 i 2a^{2}i . So its a imaginary number.

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