Understanding Re: Definition, Equations, and Solutions - Math Homework 2a

[kramer733]

Homework Statement

http://people.math.carleton.ca/~mezo/A6math1102-11.pdf
number 2a)

Homework Equations

The Attempt at a Solution

I just need help knowing what Re means. I've never seen it before and the prof didn't mention it.

 

[kylem]

"real part of", it is defined in question 2a:

where Re(a + bi) = a for a; b 2 R

 

[kramer733]

Thanks. But now I'm confused at the problem.I'm not sure how to confirm the real parts.

 

[Deveno]

<v,w> is going to be some complex number. take its real part.

for example:

<(2+3i,4-5i),(3,1-i)> = (2+3i)(3) + (4-5i)(1+i) = 6+9i + (4-(-5) + (4 - 5)i)

= 6+9i + 9-i = 15+8i, and the real part of this is 15.

 

[Ray Vickson]

<v,w> is going to be some complex number. take its real part.

for example:

<(2+3i,4-5i),(3,1-i)> = (2+3i)(3) + (4-5i)(1+i) = 6+9i + (4-(-5) + (4 - 5)i)

= 6+9i + 9-i = 15+8i, and the real part of this is 15.

You can also get the real part of a complex quantity z: $$\mbox{Re}(z) = \frac{1}{2}(z + \bar{z}),$$ where $\bar{z}$ is the complex conjugate of z.

RGV