Yes, 23 has an inverse mod 1000 because gcd(23, 1000) = 1 (i.e. they are coprime).
Let <em>x</em> be the inverse. Then <em>x</em> is such that
23<em>x</em> ≡ 1 (mod 1000)
Use the Euclidean algorithm to solve for <em>x</em> :
1000 = 43×23 + 11
23 = 2×11 + 1
→ 1 ≡ 23 - 2×11 (mod 1000)
→ 1 ≡ 23 - 2×(1000 - 43×23) (mod 1000)
→ 1 ≡ 23 - 2×1000 + 86×23 (mod 1000)
→ 1 ≡ 87×23 - 2×1000 ≡ 87×23 (mod 1000)
→ 23⁻¹ ≡ 87 (mod 1000)
So,
If the number in the ten-thousandth's place is greater than or equal to 5, then round up. If not, round down.
0.1325: Note the 5. We round up.
0.1325 --> 0.133
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He would have to work 24 weeks to get the same amount from each job.
Answer:
3i
Step-by-step explanation:
3i x 3i = -9
-3i x -3i = -9
Therefore the square root of -9 is 3i or -3i
