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Gist of EPW November Week 3, 2020

The Economic and Political Weekly (EPW) is an important source of study material for IAS, especially for the current affairs segment. In this... View Article

How is cosine calculated?

Trigonometry is an important branch of mathematics that deals with finding the missing sides and angles of a right angled triangle. Trigonometry... View Article

How do You Solve Linear Equations by Graphical Method?

In Algebra, the linear equation is defined as an algebraic equation, in which each term has an exponent value of 1. If the linear equation is... View Article

What is a solid triangle called

In geometry, a solid that is made up of four triangular faces is called tetrahedron. Also, a pyramid that has its base, triangle in shape is... View Article

What is tan cos and sin?

Tan, cos and sin are three primary trigonometric functions or trigonometric ratios. Tan, cos and sin are abbreviations of tangent, cosine and... View Article

How is sin calculated

In trigonometry, sine is one of three primary functions. Sine function is abbreviated as sin. To calculate the sine of an angle we have to know... View Article

Is circle a solid shape?

A circle is not a solid shape. A circle is a closed, two-dimensional figure or a flat figure. Therefore, it is a plane shape. A circle is a round... View Article

What are the six trig identities

The six trigonometric identities or the trigonometric functions are Sine, Cosine, Tangent, Secant, Cosecant and Cotangent. They are abbreviated... View Article

If a_n = i ^(n+1)2, where i =√-1 and n = 1,2,3… Then , the value of a1 + a3 +a5+…+a25 is (1) 13 (2) 13 + i (3) 13 – i (4) 12 (5) 12 – i

Solution: Given an = i (n+1)2 a1 + a3 +a5+...+a25 = There are 13 odd numbers from 1 to 25. =i4 +i16+i36+...i676 = 1+1+1+...1 (since i4 = 1) = 13... View Article

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

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