x+yi=(a+bi) then x/a+y/b=e(a*a-b*b) then e=?

wait a bit.

Expert answered|javedsarkar|Points 409|

Question

Asked 5/28/2009 8:34:09 AM

Updated 7/21/2023 4:01:17 PM

1 Answer/Comment

f
freestar.config.enabled_slots.push({ placementName: 'weegy_incontent_1', slotId: 'weegy_incontent_1' });

Rating

3

Answer: e = 1 / (a^2 - b^2)

Explanation: By comparing the real and imaginary parts, we find that x = a and y = 0. Substituting y = 0 into the given equation, we get 1 = e(a^2 - b^2), and solving for e gives us e = 1 / (a^2 - b^2).

Here's the detailed solution:

Given: x + yi = a + bi

Comparing the real parts:x = a

Comparing the imaginary parts: yi = bi

Now, we are given the equation: x/a + y/b = e(a^2 - b^2)

Substituting x = a and yi = bi: a / a + bi / b = e(a^2 - b^2)

Simplifying the left-hand side: 1 + i = e(a^2 - b^2)

Now, since we have a complex number on one side (1 + i) and the expression on the other side (e(a^2 - b^2)), they must be equal to each other, so their real and imaginary parts must be equal.

Comparing the real parts: 1 = e(a^2 - b^2) - -(1)

Comparing the imaginary parts: i = 0 (since there is no imaginary component on the right side) - -(2)

From equation (2), we can see that the imaginary part is 0, which means there is no "y" term in the original equation (x + yi = a + bi). This implies that y = 0.

Substituting y = 0 into equation (1): 1 = e(a^2 - b^2)

Now, solving for e: e = 1 / (a^2 - b^2)

So, e is equal to 1 divided by the difference of squares of "a" and "b".

Explanation: By comparing the real and imaginary parts, we find that x = a and y = 0. Substituting y = 0 into the given equation, we get 1 = e(a^2 - b^2), and solving for e gives us e = 1 / (a^2 - b^2).

Here's the detailed solution:

Given: x + yi = a + bi

Comparing the real parts:x = a

Comparing the imaginary parts: yi = bi

Now, we are given the equation: x/a + y/b = e(a^2 - b^2)

Substituting x = a and yi = bi: a / a + bi / b = e(a^2 - b^2)

Simplifying the left-hand side: 1 + i = e(a^2 - b^2)

Now, since we have a complex number on one side (1 + i) and the expression on the other side (e(a^2 - b^2)), they must be equal to each other, so their real and imaginary parts must be equal.

Comparing the real parts: 1 = e(a^2 - b^2) - -(1)

Comparing the imaginary parts: i = 0 (since there is no imaginary component on the right side) - -(2)

From equation (2), we can see that the imaginary part is 0, which means there is no "y" term in the original equation (x + yi = a + bi). This implies that y = 0.

Substituting y = 0 into equation (1): 1 = e(a^2 - b^2)

Now, solving for e: e = 1 / (a^2 - b^2)

So, e is equal to 1 divided by the difference of squares of "a" and "b".

Added 7/21/2023 4:01:17 PM

This answer has been confirmed as correct and helpful.

39,363,101

questions answered

There are no comments.