# What is the conjugate of $\frac{1}{2}+ \frac{3}{2}i$?

What is the conjugate of $\dfrac{1}{2}+ \dfrac{3}{2}i$?

Firstly, what is conjugation? And secondly, can you should the steps to doing this?

"$i$" is the imaginary unit.

-
$\frac{1}{2}-\frac{3}{2}i$ – Potato Feb 3 '12 at 2:22

5
Google is your friend! – JavaMan Feb 3 '12 at 3:48

## 1 Answer

The conjugate of $a+bi$ is $a-bi$.

-
What is conjugate? How did you arrive at this answer? :) – David Feb 3 '12 at 1:29

4
– Jonas Meyer Feb 3 '12 at 1:32

1
What Joe said is of course correct. If you want a more geometric idea, you can think of it as reflection across the x-axis in the complex plane. – Jackson Walters Feb 3 '12 at 1:34

4
@David There is nowhere to arrive from, conjugation is just defined this way. period. – Christian Rau Feb 3 '12 at 2:15
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 6, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "english_confidence": 0.9072457551956177, "perplexity_flag": "middle"}