The number(s) written inside the () of a function like abs() or sqrt() or pow() are called as ________________
Answers
Explanation:
important concept for numbers, either real or complex is that of absolute value. Recall that the absolute value |x| of a real number x is itself, if it's positive or zero, but if x is negative, then its absolute value |x| is its negation –x, that is, the corresponding positive value. For example, |3| = 3, but |–4| = 4. The absolute value function strips a real number of its sign.
For a complex number z = x + yi, we define the absolute value |z| as being the distance from z to 0 in the complex plane C. This will extend the definition of absolute value for real numbers, since the absolute value |x| of a real number x can be interpreted as the distance from x to 0 on the real number line. We can find the distance |z| by using the Pythagorean theorem. Consider the right triangle with one vertex at 0, another at z and the third at x on the real axis directly below z (or above z if z happens to be below the real axis). The horizontal side of the triangle has length |x|, the vertical side has length |y|, and the diagonal side has length |z|. Therefore,
|z|2 = x2 + y2.
(Note that for real numbers like x, we can drop absolute value when squaring, since |x|2 = x2.) That gives us a formula for |z|, namely,
the absolute value of z is the square root of (x^2+y^2)
The unit circle.
Some complex numbers have absolute value 1. Of course, 1 is the absolute value of both 1 and –1, but it's also the absolute value of both i and –i since they're both one unit away from 0 on the imaginary axis. The unit circle is the circle of radius 1 centered at 0. It include all complex numbers of absolute value 1, so it has the equation |z| = 1.
A complex number z = x + yi will lie on the unit circle when x2 + y2 = 1. Some examples, besides 1, –1, i, and –1 are ±√2/2 ± i√2/2, where the pluses and minuses can be taken in any order. They are the four points at the intersections of the diagonal lines y = x and y = x with the unit circle. We'll see them later as square roots of i and –i.
Answer:
The ΔA′BC′ whose sides are 43 of the corresponding sides of ΔABC can be drawn as follows:
Step 1: Draw a ΔABC with side BC=6cm,AB=5cm,∠ABC=60∘
Step 2: Draw a ray BX making an acute angle with BC on the opposite side of vertex A.
Step 3: Locate 4 points, B1,B2,B3,B4 on line segment BX.
Step 4: Join B4C and draw a line through B3, parallel to B4C intersecting BC at C′.
Step 5: Draw a line through C′ parallel to AC intersecting AB at A′.
The triangle A′BC′ is the required triangle.