Your result is right, but you might write it in the form ##-\frac{1}{8}- \frac{1}{8} i##53Mark53 said:Homework Statement
How would I go about solving 1/z=(-4+4i)
The answer that I keep on getting is wrong
The Attempt at a Solution
[/B]
What I did
z=1/(-4+4i)x(-4-4i)/(-4-4i)
z=(-4-4i)/(16+16i-16i-16i^2)
z=(-4-4i)/32
z=-1/8-i/8
This is the answer that I got however it says that it is wrong. I am unsure what else I can do
Thanks for any help
Thanks! I thought I was right, the online quiz that we have must have a mistake thenehild said:Your result is right, but you might write it in the form ##-\frac{1}{8}- \frac{1}{8} i##
No, it was there. This is what the OP wrote:chwala said:Complex numbers ##z##, have to be expressed in the form ##z= a+bi##, where ##a, b##, are real numbers, this was missing in your solution, the ##"i"##
z=-1/8-i/8
Maybe you should write 0.125 instead of 1/8.53Mark53 said:Thanks! I thought I was right, the online quiz that we have must have a mistake then
Complex numbers are numbers that are expressed in the form of a+bi, where a and b are real numbers and i is the imaginary unit, defined as the square root of -1. These numbers are used to represent both real and imaginary quantities in mathematics and science.
Real numbers are the numbers that we use in our everyday lives, such as 1, 2, 3, etc. They can be plotted on a number line and have a single value. Imaginary numbers, on the other hand, involve the use of the imaginary unit i and cannot be plotted on a number line. They are commonly used in mathematics and physics to represent quantities that cannot be expressed using real numbers.
To add or subtract complex numbers, you simply add or subtract the real parts and the imaginary parts separately. For example, (3+5i)+(2-4i) = (3+2)+(5i-4i) = 5+i. Similarly, (3+5i)-(2-4i) = (3-2)+(5i+4i) = 1+9i.
To multiply complex numbers, you can use the FOIL method, just like you would with binomials. For example, (3+5i)(2-4i) = 6-12i+10i-20i^2 = 6-2i-20(-1) = 26-2i. To divide complex numbers, you can use the conjugate of the denominator to eliminate the imaginary unit in the denominator. For example, (3+5i)/(2-4i) = (3+5i)(2+4i)/(2-4i)(2+4i) = (6+12i+10i+20i^2)/(4+8i-8i-16i^2) = (6+22i+20(-1))/(4+16) = (26+22i)/20 = 13/10 + 11i/10.
Complex numbers have various applications in fields such as engineering, physics, and economics. They are used to represent and analyze alternating currents in electrical circuits, model vibrations and waves, and solve differential equations. They also have applications in signal processing, control systems, and financial analysis.