Soal Matematika D-3 Monbukagakusho.

Diketahui $\alpha =2; \beta =\sqrt{3}+i$; dan $\gamma =1+i; \left ( i^{2}=-1 \right )$. Temukan nilai mutlak r dan besar sudut $\theta$ dari $\frac{\alpha @plus;\beta }{\gamma } \left ( -\pi < \theta \leq \pi \right )$.

Solusi:



Bilangan kompleks pada umumnya dinyatakan sebagai penjumlahan dua suku (a+bi), dengan suku pertama adalah bilangan riil, dan suku kedua adalah bilangan imajiner. Misalnya, 2+3i.

Dengan menganggap bahwa: dan , maka


Untuk mempersingkat penulisan, bentuk di atas juga sering ditulis sebagai .




sehingga diperoleh
(Sudut theta sebenarnya bisa juga , tapi karena sin yang negatif dan cos positif, maka theta harus  berada di kuadran IV. Jadi,  bukan penyelesaian)




Jadi, dan

Mental Health and the Heart - Reader's Digest

                At least one in five people who get heart bypass surgery experiences depression, which has been shown to increase the risk of developing further cardiac problems. But cognitive behavioural therapy (CBT) – a type of talk therapy – can help. In one study, published in the journal Archives of General Psychiatry, 71 percent of the patients with a recent history of heart bypass surgery undergoing CBT were free from depression after just three months of treatment. In contrast, just one third of patients in a control group saw their depression lift.

Beth Howard

Help For The Hopeless

                About 20 percent of people suffering from depression get no relief from either medication or psychotherapy. But Harvard Medical School researchers found that stimulation from electrodes implanted in the brain produced a 22-percent improvement in symptoms after eight weeks (compared with a 3-percent improvement for patients receiving a sham treatment).


source: Reader's Digest - rdasia.com
picture: google.com 

Advances in Allergies - Reader's Digest

Lower Your Risk, Put Down Your Drink

                 If you want to avoid allergies, cut back on alcohol. A Danish study of 5870 women found that the risk of nonseasonal allergies (such as sniffles due to dust mites or cats) increased three percent for each drink consumed weekly. The study showed that women who drank more than 14 alcoholic beverages a week were 78 percent more likely to develop these allergies than were those who had less than one drink weekly. Unclear: whether drinking has the same nose-clogging effect in men.

Spray Away Your Cough

                Allergies plus postnasal drip equals chronic cough. Here’s an easy fix: Use a nasal spray. Among patients who’d suffered a cough caused by postnasal drip for an average of seven years, a combo of an antihistamine spray and a steroid spray brought relief for 76 percent of subjects.

                “Doctors prescribe nasal spray for nasal congestion but not for a cough,” says Dr Brian Levine, who’s with the Cough Center in Laguna Hills, California. Talk to your doctor if you clear your throat often, get hoarse, have a sore throat or simply suffer from a chronic cough. “Combination nasal-spray therapy can dramatically improve all these conditions,” says Levine.

A Tab Instead of a Shot?

                While pills and sprays calm allergy symptoms, only immunotherapy (allergy shots) offers lasting relief – and may prevent the development of allergy-triggered asthma. Yet very few of those who could benefit go through the trouble and time (it can take years of shots). So this news is exciting: In a recent German study, a daily tablet of grass pollen placed under the tongue reduced hay-fever symptoms in kids by 24 percent over placebo treatment, and asthma symptoms by 64 percent.  Under-the-tongue tablets and drops have been used in Europe for decades. If the new results are borne out, ‘sublingual immunotherapy “ may be available in the near future.

E.R.

source: Reader's Digest - rdasia.com

picture: google.com 

Health Smart - Reader's Digest

FIGHTING HEAT STRESS

                The biggest health threat of the 21st century? Climate change, according to a report from The Lancet and University College London. In Europe, the 2003 heatwave killed thousands, and in Asia, searing wheather each summer kills hundreds in India and Pakistan. Researchers said green-house-gas emissions make a repeat likely. And experts note that night-time temperatures across North America have been unusually high for the past few years. But there’s simple way to fight the stress to our bodies caused by heat – especially if there’s no relief at night: Drink extra water. And if you feel dizzy or nauseated (sign of heat exhaustion), immediately sponge yourself with cool water.

Meryl Davids – Landau

TRIMMING THE FAT IN YOUR LIVER

                Even fat that you don’t see can kill you: If you’re over weight and have diabetes, doctors say, you probably have a fatty liver – which raises your risk of developing ills that go beyond just that organ. (Heart disease is but one example.) But there are ways to trim the fat. Researchers at Johns Hopkins University found that moderate biking, walking or running three times a week, combined with resistance traning, cut the fat in people’s livers by as much as 40 percent. “It’s an added reason to exercise,” says Karry Stewart, lead investigator of the study.

Elena Rover

PHYSICAL ACTIVITY: THE MIDDLE-AGE ELIXIR

                It’s never too late to enjoy the health benefits of exercise: Men who became very physically active beginning only at age 50 cut their risk of dying early by 32 percent, according to a Swedish study published in the journal BMJ. (Early-mortality rates of same-age men who’ve always been highly active were used as a baseline.) This longevity boon – comparable with that associated with quitting smoking – kicks in only after five years of maintaining an active lifestyle, explain researchers. Still, three hours of sports or heavy gardening a week was enough to do the trick.

E.R.

AIM FOR 55 - 65 HEARTBEATS PER MINUTE

                Athletes pride themselves on it: a lower resting heart rate indicates they’re in good physical shape, so their hearts don’t have to pump as hard. That usually means a lower risk of heart problems. “At a higher rate, the heart needs more oxygen, stressing the cardiovascular system,” says Dr Kim Fox, of the Royal Brompton Hospital in London. The best way to reduce your rate? Exercise.

ARCHING BODY? CHECK YOUR SINUSES

                The aches and pains in your body could be all in your head – specifically, your sinuses. It’s even possible that your arthritis, fibromyalgia or chronic fatigue syndrome is a misdiagnosis of pain and tiredness resulting from recurring sinus infections, says Professor Alexander Chester of the Georgetown University Medical Center. He estimates that half of people with chronic sinusitis have symptoms such as serious body aches and fatigue. The pain can be all over but more pronounced in spots such as the shoulders, neck and hips.

source: Reader's Digest - rdasia.com

picture: google.com 

Hafalan Shalat Delisa - karya tere-liye

Assalamu 'alaikum warahmatullahi wabarokatuh.

Hi everyone!

A few weeks ago (exactly about 30 weeks ago), I have read a great book that entitled Hafalan Shalat Delisa. It's a story about a very young girl called Delisa, she lives in Aceh and unfortunately she face the great tsunami disaster that kill her entire family except her father. In a few day after the tsunami, Delisa must survive to live with a broken leg until someone find her.

This story is very touching, you need one big box tissue when you read it. :p

And I just copied some words from this book that had great meaning, personally. But I don't translate it to English because I'm afraid I will reduce it's true meaning (alias malas).

Big thanks to Allah SWT who let me live to read this book, Tere-liye who write this book, and my best friend Akbar Khashemi Hamzah who lent me this book.

Indah sekali, kerudung itu sungguh bagai terbuat dari air. Ya Allah, jadikan ia sebagai kerudung yang akan dipakai "perhiasan terbaikku". Pinjamkan ia di atas kepala kekasih dunia-akheratku.

Kau memiliki lebih banyak teman dibandingkan seluruh dunia dan seisinya.

Semua manusia yang masih memiliki hati di dunia ini akan selalu merasa dekat dengan siapa saja yang kebetulan sedang tertimpa musibah.

Sungguh setelah kesulitan akan ada kemudahan! Sungguh setelah kesulitan akan ada kemudahan. Itu janjiMu yang tertoreh di atas kitab suci. Sungguh tak ada keraguan di sana! Bagaimanalah orang-orang tak mempercayainya? Itu kata-kataMu. Janji dari Maha-Pemegang Janji!

Ya Rabb, Engkaulah alasan semua kehidupan ini. Engkaulah penjelasan atas semua kehidupan ini. Perasaan itu datang dariMu. Semua perasaan itu juga akan kembali kepadaMu. Kami hanya menerima titipan. Dan semua itu ada sungguh karenaMu....

Katakanlah wahai semua pecinta di dunia. Katakanlah ikrar cinta itu hanya karenaNya. Katakanlah semua kerinduan itu hanya karena Allah. Katakanlah semua getar-rasa itu hanya karena Allah. Dan semoga Allah Yang Maha Mencinta, yang menciptakan dunia dengan kasih sayang mengajarkan kita tentang cinta sejati.

Semoga Allah memberikan kesempatan kepada kita untuk merasakan hakikatNya. Semoga Allah sungguh memberikan kesempatan kepada kita untuk memandang wajahNya. Wajah yang akan membuat semua cinta dunia layu bagai kecambah yang tidak pernah tumbuh. Layu bagai api yang tidak pernah panas membakar. Layu bagai sebongkah es yang tidak membeku.