Complex Numbers

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4 Terms

1
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What is the set of complex numbers defined as?

C = {a + bi : a ∈ R and b ∈ R} .

2
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The complex conjugate z ̄ of a complex number z = a + bi given by?

z ̄ = a − bi.

3
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For z ∈ C\ {0} a non-zero complex number, what is the inverse of z given by?

z−1 = (1/zz-)z-

4
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What is the quotient of two complex numbers α = a + bi and β = c + di, with β ̸= 0?

αβ−1 = α/β = (1/ββ-)αβ-