# Thread: divide and express equation in standard form

1. ## divide and express equation in standard form

divide and express the following equation in standard form, can someone explain to me how to do this.

2. You must multiply by the conjugate.
$\displaystyle \frac{1}{a+bi}= \frac{1}{a+bi}\cdot \frac{a-bi}{a-bi} = \frac{a-bi}{a^2-b^2}$
$\displaystyle \frac{a}{a^2-b^2}-\frac{bi}{a^2-b^2}$
You can also use the polar form (Euler notation)
$\displaystyle *re^{i\theta}$
In your case the top part is $\displaystyle 2e^{0}=2$ and the bottom part $\displaystyle \sqrt{3^2+1}e^{i arctan\frac{-1}{3}} \simeq \sqrt{10}e^{-0.3218i}$ You are thus going to end with $\displaystyle \frac{2}{ \sqrt{10}e^{-0.3218i}}=\frac{2e^{0.3218i}}{ \sqrt{10}}$ $\displaystyle \frac{2}{ \sqrt{10}}(cos(0.3218)+isin(0.3218))$

3. Thanks for the fast reply, can you verify if this is correct

4. Replace $\displaystyle i^2$by its value and simplify and ... you're done.

5. ok thanks, but I wasn't given a value for i

6. $\displaystyle *i = \sqrt{-1}$*This is among the most important number in mathematics. Remember its definition.

7. ok thank you very much for your assistance

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