If z=3−5i, find |z|.
1 answer:
Answer:
Step-by-step explanation:
The absolute value of z is the distance between the point graphed from the complex number and the origin on a complex plane. In a complex plane, the x axis is replaced by R, real numbers, and the y axis is replaced by i, the complex part of the complex number. Our real number is positive 3 and the complex number is -5, so we go to the right 3 and then down 5 and make a point. Connect that point to the origin and then connect the point to the x axis at 3 to construct a right triangle that has a base of 3 and a length of -5. To find the distance of the point to the origin is to find the length of the hypotenuse of that right triangle using Pythagorean's Theorem. Therefore:
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Answer:
Step-by-step explanation:
If we are given a function <em>f</em> and we want to shift it <em>a</em> units horizontally, the resulting function will be f(<em>x</em> - <em>a</em>), where a positive <em>a</em> is a shift rightwards and a negative <em>a</em> is a shift leftwards.
We have the function:
And we want to shift it two units to the left.
Since we want to shift it two units to the left, <em>a</em> = -2. Therefore, our new function, let's call it <em>g</em>, must be f(<em>x</em> - (-2)) or f(<em>x</em> + 2). Substitute:
Simplify. Expand:
Combine like terms. Hence:
Answer:
The equation is