Here you will learn what is the division of complex numbers with examples. Let’s begin – Division of Complex Numbers The division of a complex number \(z_1\) by a non-zero complex number \(z_2\) is defined as the multiplication of \(z_1\) by the multiplicative inverse of \(z_2\) and is denoted by \(z_1\over z_2\). Thus, \(z_1\over z_2\) …
Here you will learn multiplication of complex numbers and its properties with examples. Let’s begin – Multiplication of Complex Numbers Let \(z_1\) = \(a_1 + ib_1\) and \(z_2\) = \(a_2 + ib_2\) be two complex numbers. Then the multiplication of \(z_1\) with \(z_2\) is denoted by \(z_1 z_2\) and is defined as the complex number …
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Here you will learn subtraction and addition of complex numbers and its properties with examples. Let’s begin – Addition of Complex Numbers Let \(z_1\) = \(a_1 + ib_1\) and \(z_2\) = \(a_2 + ib_2\) be two complex numbers. Then their sum \(z_1 + z_2\) is defined as the complex number \((a_1 + a_2)\) + i\((b_1 …
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Here you will learn what is the complex number class 11 and equality of complex numbers with examples. Let’s begin – Complex Number Class 11 If a, b are two real numbers, then a number of the form a + ib is called aa complex number. Example : 7 + 2i, -1 + i, 3 …
Here you will learn complex number i (iota) and integral powers of iota with examples. Let’s begin – Integral Powers of Iota (i) Positive Integral Powers of iota(i) : We have, i = \(\sqrt{-1}\) \(\therefore\) \(i^2\) = -1 \(i^3\) = \(i^2\) \(\times\) i = -i \(i^4\) = \((i^2)^2\) = \((-1)^2\) = 1 In order to …
Here you will learn formula to find middle term in binomial expansion with examples. Let’s begin – Middle Term in Binomial Expansion Since the binomial expansion of \((x + a)^n\) contains (n + 1) terms. Therefore, (1) If n is even, then \({n\over 2} + 1\) th term is the middle term. (2) If n …
Here you will learn formula for binomial theorem of class 11 with examples. Let’s begin – Formula for Binomial Theorem If x and a are real numbers, then for all n \(\in\) N. \((x + a)^n\) = \(^{n}C_0 x^n a^0\) + \(^{n}C_1 x^{n – 1} a^1\) + …………… + \(^{n}C_r x^{n – r} a^r\) + …………… …
Here you will learn formula to find the general term in binomial expansion with examples. Let’s begin – General Term in Binomial Expansion We have, \((x + a)^n\) = \(^{n}C_0 x^n a^0\) + \(^{n}C_1 x^{n – 1} a^1\) + …………… + \(^{n}C_r x^{n – r} a^r\) + …………… + \(^{n}C_n x^0 a^n\) We find that …
Here you will learn how to find image of a point in a plane formula with examples. Let’s begin – Image of a Point in a Plane Let P and Q be two points and let \(\pi\) be a plane such that (i) line PQ is perpendicular to the plane \(\pi\) and, (ii) mid-point of …
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Here you will learn how to find equation of plane containing two lines with examples. Let’s begin – Equation of Plane Containing Two Lines (a) Vector Form If the lines \(\vec{r}\) = \(a_1 + \lambda\vec{b_1}\) and \(\vec{r}\) = \(a_2 + \mu\vec{b_2}\) are coplanar, then \(\vec{r_1}\).(\(\vec{b_1}\times \vec{b_2}\)) = \(\vec{a_2}\).(\(\vec{b_1}\times \vec{b_2}\)) or, [\(\vec{r}\) \(\vec{b_1}\) \(\vec{b_2}\)] = [\(\vec{a_2}\) …
