Hi there!
When I started teaching Business English at a language school more than scores of years ago, I was absorbed in improvising a slew of imaginary conversations or dialogues during my preparation time.
Creating various kinds of characters helped me wing it to several types of students, such as a persistent interpellator-type student, a demanding one like a complainer, a reticent one like the clam-up shell, and whatnot.
Imaginary fears, though seldom hog-tied my teaching, contributed to impeccable class preparations with a glossary of jargon, and buzz words, including repartees. My “Let-me-wing-it” attitudes in the classroom were admittedly supported by consummate behind-the-scenes preps.
Albert Einstein is quoted as saying, “Out of clutter, find simplicity.” The class lesson shall be converged to simplicity yet be backed up and enhanced by scrutinizing scad of materials. Imaginations lead to creations, thus creating sublime quality of teaching before reaching overkill.
Today, let me challenge a complex number word problem dealing with actual and imaginary numbers.
Evaluate the complex number \(\frac{1 + \sqrt{-6}}{\sqrt{-2}}\)
Here is my solution to the problem.
\(\frac{1 + \sqrt{-6}}{\sqrt{-2}}\)
\(= \frac{1 + \sqrt{6}i}{\sqrt{2}i}\)
\(= \frac{(1 + \sqrt{6}i)・\sqrt{2}i}{\sqrt{2}i・\sqrt{2}i}\)
\(= \frac{\sqrt{2}i + \sqrt{6・2\,\,}\,i^{2}}{2i^{2}}\)
\(= \frac{\sqrt{2}i + \sqrt{2・2・3\,\,\,}・(-1)}{2・(-1)}\)
\(= \frac{\sqrt{2}i + 2\sqrt{3}・(-1)}{2・(-1)}\)
\(= \sqrt{3} – \frac{\sqrt{2}}{2}i\)
Stay tuned, and expect to see my next post.
Keep well.
Frank Yoshida
￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣
【グローバルビジネスで役立つ数学】でもっと学習する b＾＾)
【参考図書】『もう一度高校数学』（著者：高橋一雄氏）株式会社日本実業出版社
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