Square Me Away
If and are integers satisfying the equation above, then find the value of .
Notation:
- is the imaginary unit .
- is the absolute value function .
The answer is 1.
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1 solution
Expanding we get a 2 − b 2 + 2 i a b = 7 + 2 4 i .
Comparing real and imaginary parts :
a 2 − b 2 = 7 and a b = 1 2
Solving we get a = 4 , b = 3 or a = − 4 , b = − 3 .
∣ a ∣ − ∣ b ∣ = 1 .