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Find the value of x and y for which (3 + 4i) x2 – (4 – 3i) y = 3x – 4y + 6i, where x, y ∈ R.

Find the value of x and y for which (3 + 4i) x2 – (4 – 3i) y = 3x – 4y + 6i, where x, y ∈ R. Correct Answer <span class="math-tex">\(x = 0,\;1\;and\;y = 2,\;\frac{2}{3}\)</span>

CONCEPT:

Two complex number z1 = a1 + ib1 and z2 = a2 + ib2 are equal if and only if their real and imaginary parts are equal individually.

I.e. z1 = z2

⇒ Re(z1) = Re(z2) and Im (z1) = Im(z2)

CALCULATION:

Given (3 + 4i) x2 – (4 – 3i) y = 3x – 4y + 6i

⇒ 3x2 – 4y = 3x – 4y

⇒ 3x2 - 3x = 0

∴ x2 - x = 0

⇒ x = 0, 1

Now we will equate the imaginary part.

∴ 4x2 + 3y = 6

So, when x = 0; y = 2 and when x = 1, y = 2 / 3

Related Questions

Let x̅1 and x̅2 (where x̅2 > x̅1) be the means of two sets comprising n1 and n2 (where n2 < n1) observations respectively. If x̅ is the mean when they are pooled, then which one of the following is correct?
λ এর কোন মানের জন্য 4î+2ĵ-3k^ এবং λî-3ĵ+2k^ ভেক্টরদ্বয় পরস্পর লম্ব হবে?
î + ĵ + k^ এবং 3î + 3ĵ - 6k^ ভেক্টরদ্বয়ের মধ্যবর্তী কোণ কত?
A→=2î এবং B→=3î হলে ভেক্টর দুটির মধ্যবর্তী কোন কোনটি?
The area of the square, one of whose diagonals is 3î + 4ĵ is
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There are three numbers A, B, and C such that if we increase the value of C by 15, we get a number which is equal to the value of B. Also, it is known that the value of A is three times the value of C. If the value of A is twice the value of B, then find the difference between the values of A and C.
Consider the pseudocode given below. The function DoSomething() takes as argument a pointer to the root of an arbitrary tree represented by the leftMostChild-rightSibling representation. Each node of the tree is of type treeNode. typedef struct treeNode* treeptr; struct treeNode {              treeptr leftMostChild, rightSibling; }; int DoSomething (treeptr tree) {              int value=0;              if (tree != NULL) {              if (tree->leftMostChild == NULL)              value = 1;    else               value = DoSomething(tree->leftMostChild);               value = value + DoSomething(tree->rightSibling);     }               return(value); } When the pointer to the root of a tree is passed as the argument to DoSomething, the value returned by the function corresponds to the 
Read the passage carefully and select the best answer to each question out of the given four alternatives.
Public opinion may be passive and false or active and real. It is claimed in theory that all governments are ultimately based on the opinion or sanction of the governed. But we find that in practice the people's rights are often trodden down and tyranny and oppression are allowed to continue. The government does it not because the people want it to do so but because they are too idle, too uneducated and too disunited or timid to oppose the govern ment. Such public opinion is passive and false and not an active verdict. But when we find people alert, intelligent and determined to let the government know their will, when they want to exercise actively their voice in the management of their country, we have an instance of true or active public opinion. True public opinion is formed by and expressed through the press, the platform, political parties and educational institutions. These have sacred duties to perform, duties on which depends the ultimate good of the entire community. The press today wields a tremendous influence, So it should support the causes and move ments and condemn the wrong one's and thus teach people to form correct opinion. A free and fair press ventilates the grievances of the public. Thus a healthy relationship develops between the people and the government through out an unbiased press. Political parties also help to create and regulate opinions. No less important part is played by the educational Institutions which train the minds of the young people who will be the citizens of tomorrow. It has been said that modern Germany and China have been made by their universities. It is necessary that the young and the growing minds should imbibe the spirit of fellow-feeling, the spirit of tolerance, the habit of compromise, and show due regard for the feelings and opinion of others without which a democratic society cannot function, let alone succeed. When there is true awakening of the people, we shall have the real and conscious public opinion. And justice will reign on earth and truly will the voice of the people be the voice of God.
Which of the following is not the reason for the oppression caused to general public by the running government in the country?
Read the passage carefully and select the best answer to each question out of the given four alternatives.
Public opinion may be passive and false or active and real. It is claimed in theory that all governments are ultimately based on the opinion or sanction of the governed. But we find that in practice the people's rights are often trodden down and tyranny and oppression are allowed to continue. The government does it not because the people want it to do so but because they are too idle, too uneducated and too disunited or timid to oppose the govern ment. Such public opinion is passive and false and not an active verdict. But when we find people alert, intelligent and determined to let the government know their will, when they want to exercise actively their voice in the management of their country, we have an instance of true or active public opinion. True public opinion is formed by and expressed through the press, the platform, political parties and educational institutions. These have sacred duties to perform, duties on which depends the ultimate good of the entire community. The press today wields a tremendous influence, So it should support the causes and move ments and condemn the wrong one's and thus teach people to form correct opinion. A free and fair press ventilates the grievances of the public. Thus a healthy relationship develops between the people and the government through out an unbiased press. Political parties also help to create and regulate opinions. No less important part is played by the educational Institutions which train the minds of the young people who will be the citizens of tomorrow. It has been said that modern Germany and China have been made by their universities. It is necessary that the young and the growing minds should imbibe the spirit of fellow-feeling, the spirit of tolerance, the habit of compromise, and show due regard for the feelings and opinion of others without which a democratic society cannot function, let alone succeed. When there is true awakening of the people, we shall have the real and conscious public opinion. And justice will reign on earth and truly will the voice of the people be the voice of God.
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