<p>Hi,</p>
<p>I’m using barron’s 2008 math 2 book to prepare for my iic. The typos in the “graphing complex numbers” section is absolutely killing me. </p>
<p>Questions:</p>
<p>Is the mod of a complex number the distance from the origin on the complex number plane? sqrt(a^2+b^2)</p>
<p>Are the graphs of conjugates the reflections across the x-axis (the book said y-axis :S )</p>
<p>Is the product of conjugates the square of the modulus? (a^2+b^2)</p>
<p>thanks!</p>
<p>Okay, just so you know, that stuff will not show up on the Math II; the only time I’ve ever seen it is in my IB Math HL class.</p>
<p>The modulus of a +bi = |a + bi| = sqrt (a^2 + b^2) (that’s just the way it’s defined) And it is the distance from the origin to the point.</p>
<p>In terms of the graphs, the horizontal axis is your real component, while your vertical axis if your imaginary component.
If you have 3 - i and 3 + i, then they…hm, should be reflections across the x-axis I’m thinking…</p>
<p>(3 - i)(3 + i) = 9 - i^2 = 9 - (-1) = 9 + 1 = 10
|3 - i| = (3^2) + (-1)^2 = 9 + 1 = 10
So I would say yes, the product of conjugates is the square of the modulus.</p>
<p>Yea i checked with other sources and know for sure now Barron’s book is wrong.</p>
<p>Thanks.</p>