The complex number 5-3i is plotted on the complex plane at point (5,-3). The modulus of this complex number is approximately 5.8.
Complex numbers are mathematical entities that extend real numbers to include imaginary components, represented as "a + bi," where 'a' and 'b' are real numbers and 'i' is the imaginary unit (equal to the square root of -1). Complex numbers are used in various fields, including engineering and physics, to describe phenomena involving oscillations, electrical circuits, and quantum mechanics. They are vital for solving equations that have no real solutions and play a fundamental role in understanding complex systems and mathematical analysis, making them a valuable tool in science and engineering.
To graph the complex number 5-3i in the complex plane, you need to plot the point (5,-3). On the horizontal axis (real axis) you mark 5 and on the vertical axis (imaginary axis) you mark -3.
The modulus of a complex number a + bi is the square root of (a2 + b2). In this case, the modulus would be sqrt((5)2 + (-3)2) = sqrt(25 + 9) = sqrt(34), which is approximately 5.8 when rounded to the nearest tenth.
Learn more about Complex Numbers here:
#SPJ2
1.
Three less than 9 times a number is 21.
2.
The sum of 3 times a number and 9 is 21.
3.
The difference of 9 times a number and 3 is 21.
4.
Nine less than 3 times a number is 21.
A.
3n + 9 = 21
B.
9n – 3 = 21
C.
3n – 9 = 21