Conjugates-Complex Numbers

Algebra Level 2

Find the general form of 1 a − b i \dfrac{1}{a-bi} when represented as a sum of two fractions.

a + b i a 2 − b 2 \frac{a+bi}{a^2 - b^2} a b i a 2 − b 2 \frac{abi}{a^2 - b^2} a + b i a 2 + b 2 \frac{a+bi}{a^2 + b^2} a b + i a b \frac{ab + i}{ab}

Arjun Shrivastava by Arjun SHRIVASTAVA , 16, USA

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1 solution

Jacopo Piccione
Jul 24, 2018

1 a − b i = 1 a − b i ⋅ a + b i a + b i = a + b i a 2 + b 2 \frac{1}{a-bi}=\frac{1}{a-bi} \cdot \frac{a+bi}{a+bi} =\frac{a+bi}{a^2+b^2}

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Yup..That's the way!

Arjun SHRIVASTAVA - 2 years, 10 months ago

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