Bissoy.com
Doctors Medicines MCQs Q&A

Let p be the conjugate of the complex number q = x + iy . Find the value of pq. 

Let p be the conjugate of the complex number q = x + iy . Find the value of pq.  Correct Answer x<span style="position: relative; font-size: 10.5px; line-height: 0; vertical-align: baseline; top: -0.5em;">2</span> + y<span style="position: relative; font-size: 10.5px; line-height: 0; vertical-align: baseline; top: -0.5em;">2</span>

Concept:

Conjugate of a complex number:

For any complex number z = x + iy  the conjugate z̅ is given by  z̅ = x - iy

Calculation: 

q = x + iy

As p is conjugate to q 

∴ p = x - iy

Now, pq = (x + iy)(x - iy)

pq = x2 + iy - iy - i2y2

pq = x2 + y2

∴ pq = x2 + y2

Related Questions

In the formation of Routh-Hurwitz array for a polynomial, all the elements of a row have zero values. This premature termination of the array indicates the presence of 1. a pair of real roots with opposite sign 2. complex conjugate roots on the imaginary axis 3. a pair of complex conjugate roots with opposite real parts Which of the above statements are correct?
Consider the following statements in respect of an arbitrary complex number Z: 1. The difference of Z and its conjugate is an imaginary number. 2. The sum of Z and its conjugate is a real number. Which of the above statements is/are correct?
Let S be the set of points in the complex plane corresponding to the unit circle. (That is, S = {z : |z| = 1}. Consider the function f(z) = zz∗ where z∗ denotes the complex conjugate of z. The f(z) maps S to which one of the following in the complex plane
Let f1(z) = z2 and f2(z) = $$\overline {\text{z}} $$ be two complex variable function. Here $$\overline {\text{z}} $$ is the complex conjugate of z. Choose the correct answer.
Let x(t) be a continuous time periodic signal with fundamental period T = 1 seconds. Let {ak} be the complex Fourier series coefficients of x(t), where k is integer valued. Consider the following statements about x(3t):
1. The complex Fourier series coefficients of x(3t) are {ak} where k is integer valued.
2. The complex Fourier series coefficients of x(3f) are {3ak} where k is integer valued.
3. The fundamental angular frequency of x(3t) is 6π rad/s.
For the three statements above, which one of the following is correct?
A complex function f(z) = u(x, y) + iv(x, y) and its complex conjugate, f'(z) = u(x, y) - iv(x, y) are both analytic in the entire complex plane, where z = x + iy and $${\text{i}} = \sqrt { - 1} .$$   The function f is then given by
A point z has been plotted in the complex plane, as shown in figure below.
Complex Variable mcq question image
The plot for point $$\frac{1}{{\text{z}}}$$ is
There are two rows, each containing 3 numbers. Below are some rules to be used to get the resultant number for each row separately. Use the rule from left to right for each row and find the answer to the question. Rule: 1. If an even number is followed by an even number, then the first number will be subtracted from the second. 2. If an odd number is followed by an odd number, then both will be added. 3. If an odd number is followed by an even number, then the even number will be subtracted from the square of the odd number. 4. If an even number is followed by an odd number, then the odd number will be subtracted from the even number. Row I: 9,11, 34 Row II: 16, 9, 8 What is the difference between the resultant numbers in the first row and the second row
Which is the correct code that returns a complex number that is the complex conjugate of this one?
The product of a complex number z = x + iy and its complex conjugate $$\overline {\text{z}} $$ is