Home/Tag: Complex Numbers
11 02, 2017

Complex Proofs

By |2017-02-11T11:51:35+10:00February 11th, 2017|Tags: , , |0 Comments

Complex Proofs $$z\in C$$ such that $$\frac{z}{z-i}$$ is real. Show that z is imaginary. Let $$\frac{z}{z-i}=a$$, where a is real. Then $$z=a(z-i)$$ $$z=az-ai$$ $$ai=az-z$$ $$ai=z(a-1)$$ so $$z=\frac{ai}{a-1}$$ $$z=\frac{a}{a-1}i$$ Since a is real, then $$\frac{a}{a-1}$$ is real, and hence $$\frac{a}{a-1}i$$ is imaginary thus z is imaginary     [...]

2 01, 2017

Dividing Complex Numbers

By |2017-01-11T18:48:38+10:00January 2nd, 2017|Tags: , , , |0 Comments

Dividing Complex Numbers $$\overline{a+ib}=a-ib$$ worked examples Simplify (7 + 2i) ÷(3 + 3i). $$=\frac{{7 + 2i}}{{3 + 3i}}$$ rewrite in fraction form to make it simpler to see and work with $$=\frac{{7 + 2i}}{{3 + 3i}} \times \frac{{3 - 3i}}{{3 - 3i}}$$ multiply by the conjugate of the denominator [...]

1 01, 2017

Complex Numbers

By |2018-12-29T10:58:15+10:00January 1st, 2017|Tags: , |0 Comments

Complex Numbers $$z=a + bi$$ Go to the Complex Numbers forum to see more questions or ask your own Topics Covered in Complex Numbers Operations on Complex Numbers Division Of Complex Numbers Conjugate Proofs Complex Conjugate Roots Theorem Argand Diagrams Operations [...]

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