Write this complex number on the form a + bi

**MathCrusader** · October 13th 2012, 01:41 PM

I'm dealing with this problem where I'm to write the complex number below on the form a + bi.

$\frac {\sqrt{2+i}}{\sqrt{2-i}}$

I've tried writing it as

$\sqrt {\frac {2+i}{2-i}}$

Then I tried multiplying by the conjugate, writing it using polar coordinates, considering the squre root as an exponent of 0.5 etc. However, I just kept reaching a dead end. The expression is supposedly equal to

$\fr {2\sqrt{5}}{5} + \fr {i\sqrt{5}}{5}$

How do I go about?

**HallsofIvy** · October 13th 2012, 01:56 PM

You suspect have misread the answer you are supposed to get. It should be $2\sqrt{5}/5+ i\sqrt{5}/5$ or $2\frac{\sqrt{5}}{5}+ i\frac{\sqrt{5}}{5}$ either of which is equal to $\frac{2}{\sqrt{5}}+ \frac{i}{\sqrt{5}}$ .

You get that by, as you say, multiplying by the conjugate. Then "rationalize the denominator".

**Plato** · October 13th 2012, 02:12 PM

Originally Posted by MathCrusader

I'm dealing with this problem where I'm to write the complex number below on the form a + bi.
$\frac {\sqrt{2+i}}{\sqrt{2-i}}$
I've tried writing it as
$\frac {2\sqrt{5}}{5} + \frac {i\sqrt{5}}{5}$
How do I go about?

$\frac {\sqrt{2+i}}{\sqrt{2-i}}\frac {\sqrt{2-i}}{\sqrt{2-i}}=\frac {\sqrt{5}}{2-i}=\frac {2\sqrt{5}+\sqrt{5}i}{5}$

Thread: Write this complex number on the form a + bi

LinkBack

Thread Tools

Display

Write this complex number on the form a + bi

Re: Write this complex number on the form a + bi

Re: Write this complex number on the form a + bi

Similar Math Help Forum Discussions

Simplify and write the complex numbers in the form a + bi, where a and b are real

Complex number(exponential form)

When finding the argument to write a complex number in trigonometric form...

HELPP Write complex number in polar form.

How do I write arccos 4 as a + ib (complex number)?

Search Tags