MHB Is it possible to write this expression in the form $a+bi$?

  • Thread starter Thread starter Karpthulu912
  • Start date Start date
AI Thread Summary
The expression (5-i)/i can indeed be written in the form a+bi. By multiplying the expression by 1 in the form of i/i, it simplifies to (5i - i^2)/i^2. Utilizing the fact that i^2 equals -1, the expression further simplifies to -1 - 5i. Therefore, the final result is -1 - 5i. This confirms that it is possible to express (5-i)/i in the desired format.
Karpthulu912
Messages
4
Reaction score
0
so the karp is back with another question about math and well this time its not a long homework but rather a genuine question

is this possible?
(5-i)/i​
 
Mathematics news on Phys.org
If you are asking if it's possible to write this expression in the form $a+bi$, yes, it is:

$$c=\frac{5-i}{i}$$

Let's multiply this expression by $$1=\frac{i}{i}$$:

$$c=\frac{5-i}{i}\cdot\frac{i}{i}=\frac{5i-i^2}{i^2}$$

Now, using the fact that $i^2=-1$, we have:

$$c=\frac{5-i}{i}\cdot\frac{i}{i}=\frac{5i-i^2}{i^2}=\frac{5i-(-1)}{-1}=\frac{5i+1}{-1}=-1-5i$$ :D
 
Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
Back
Top