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The equation z bar z + a bar z+b=0 , b∈R represents a circle if (1) |a|^2 = b (2) |a|^2 > b (3) |a|^2 < b(4) None of these

Solution: |z+a|2 = |a|2-b This will represent a circle if |a|2-b > 0 or |a|2 >b Hence option (1) is the answer.... View Article

If |z- bar z| + |z+ bar z| = 2, then z lies on (1) a circle (2) a square (3) an ellipse (4) a line

Solution: Given Consider z = x+iy So |2iy|+|2x| = 2 2y+2x = 2 => x+y = 1 z lies on a straight line. Hence option (4) is the answer.... View Article

If (3+ i) ( z-bar z )- (2+ i) ( z-bar z) + 14i = 0, then z bar z is equal to (1) 5 (2) 8 (3) 10 (4) 40

Solution: Given ..(1) Let z = x+iy = x-iy = 2x = 2iy Substituting above values in (1) (3+i)2x-(2+i)2iy+14i = 0 6x+2ix-4iy+2y+14i = 0... View Article

If Z and ω are two complex numbers such that |Z| ≤ 1, |ω|≤ 1 and |Z – iω| = [latex]\left| Z-i\bar{\omega }\right|[/latex] = 2. Then, z is equal to (1) 1 or i (2) i or – i (3) 1 or – 1 (4) i or -1

Solution: Given |Z| ≤ 1, |ω|≤ 1. |Z - iω| = = 2. squaring |Z - iω|2 = 4 => => ..(i) Similarly => ..(ii)... View Article

If -π

Solution: If arg (z) = -π+θ Then arg = π-θ So arg = π-θ+θ = π Hence option (1) is the answer.... View Article

If Z = 4/(1-i) then bar z is equal to (where, bar z is complex conjugate of z) (1) 2(1+i) (2) 1+i (3) 2/(1-i) (4) 4/(1+i)

Solution: If Z = x+iy, then conjugate of Z is (x-iy) Z = 4/(1-i) = 4(1+i)/(1-i)(1+i) = 4(1+i)/2 = 2(1+i) = 2(1-i) Hence option (1) is... View Article

If |z1 + z2|^2 = |z1|^2 + |z2|^2 , then z1/z2 is (1) purely real (2) purely imaginary(3) zero of purely imaginary (4) Neither real nor imaginary

Solution: Given |z1 + z2|2 = |z1|2 + |z2|2 ⇒ ⇒ ⇒ ⇒ ⇒ ⇒ Thus z1/z2 is purely imaginary. Hence option (2)... View Article

What is the modulus of elasticity of steel?

Modulus of elasticity is a property that measures the resistance of materials towards deformation under load. Modulus of elasticity, also known... View Article

Is matrix multiplication associative

One of the properties of matrix multiplication is associative property of multiplication. Consider 3 matrices A, B and C, if and only if... View Article

Is matrix multiplication commutative

A binary operation that gives the product of two matrices is matrix multiplication. For the process of matrix multiplication, the total number of... View Article

What is the Symbol for Mean?

Symbol for average or mean is bar x. In statistics, we mostly come across the is the Mean of all possible values of any variable. Value of Mean... View Article

What is a Matrix in Math?

Matrix is a very useful topic that comes under linear algebra. It is an arrangement of elements, especially numbers, in a particular way. A... View Article

Why is Young’s Modulus important?

Young's modulus or the modulus of elasticity is a mechanical property that measures the tensile stiffness of a solid material. Young's modulus is... View Article

What Is The Formula To Calculate Interest

The formula to calculate the simple and compound interest are given below: Simple Interest Formula: Simple Interest (S.I) = PTR/100 Where, SI is... View Article

Is Ellipse A Conic Section

Yes, the ellipse is a conic section. It is considered as the closed type of conic section. Based on the angle between the cone and the plane... View Article

What Is The Median Of 5 And 7

The median is defined as the middle value of the given data set. The median of 5 and 7 is 6. Explanation: Since the given number of data is... View Article

Is The Mean Value Theorem The Same As Intermediate Value Theorem

No, the mean value theorem is not the same as the intermediate value theorem. The mean value theorem is all about the differentiable functions... View Article

How Do You Find The Inverse Of A Function With A Fraction

The procedure to find the inverse of a function, which contains a fraction is as follows: For example, if the given function is f(x) = 2/(x+1)... View Article

Can Sound Waves Travel In A Vacuum

No, sound waves cannot travel in a vacuum. This is because sound waves are mechanical waves that need a medium (such as air and water) to... View Article

What Is Difference Between Mean And Standard Deviation

In Maths, the mean is defined as the average of all the given values. It means that the sum of all the given values divided by the total number... View Article

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