Complex no: Where did I go wrong

Another one! I'm really sorry. This time I'm not sure where I went wrong.

Express in polar form, (1/(sqrt(21) - sqrt(7)i)*)

Conjugate, so I got (1/(sqrt(21) + sqrt(7)i))

Let z = sqrt(21) + sqrt(7)i

In modulus argument form ie. cis form, I got sqrt(30)cis(pi/6)

For the modulus of (1/(sqrt(21) - sqrt(7)i)*),

I got 1/sqrt(30)

But the answer is (sqrt(7)/14)!

Thank you very much for your time,

J.

Re: Complex no: Where did I go wrong

Quote:

Originally Posted by

**Tutu** Another one! I'm really sorry. This time I'm not sure where I went wrong.

Express in polar form, (1/(sqrt(21) - sqrt(7)i)*)

Conjugate, so I got (1/(sqrt(21) + sqrt(7)i))

Let z = sqrt(21) + sqrt(7)i

In modulus argument form ie. cis form, I got sqrt(30)cis(pi/6)

For the modulus of (1/(sqrt(21) - sqrt(7)i)*),

I got 1/sqrt(30)

But the answer is (sqrt(7)/14)!

Thank you very much for your time,

J.

In order to convert to the polar form, the complex number first needs to be in Cartesian form.

$\displaystyle \displaystyle \begin{align*} \frac{1}{\sqrt{21} - i\sqrt{7}} &= \frac{\sqrt{21} + i\sqrt{7}}{\left( \sqrt{21} - i\sqrt{7} \right) \left( \sqrt{21} + i\sqrt{7} \right)} \\ &= \frac{\sqrt{21} + i\sqrt{7}}{\left( \sqrt{27} \right)^2 + \left( \sqrt{7} \right)^2 } \\ &= \frac{\sqrt{21} + i\sqrt{7}}{34} \\ &= \frac{\sqrt{27}}{34} + i\frac{\sqrt{7}}{34} \end{align*}$

Now that it's in $\displaystyle \displaystyle \begin{align*} a + i\,b \end{align*}$ form, try converting to polars.

Re: Complex no: Where did I go wrong