You didn't say 10+12i or 10-12i
In the case of (10+12i), you would have a point in the xy plane @ x=10 and y=12
or (10,12)
In the case of (10-12i), you would have a point in the xy plane @ x=10 and y=-12
or (10,-12)
There are programs to "bend" photos with complex numbers.
Refer to the LINK and Source below.
It seems like your question is incomplete or unclear. If you're asking about "12i" in a mathematical or complex number context, "12i" represents a purely imaginary number where "i" is the imaginary unit (the square root of -1). If you meant something else or need further clarification, please provide more details!
The negative square root of -144 is -12i - that is -12 times the square root of minus 1, ie √-144 = 12√-1. The above is a complex number, which I suspect is not the answer you wanted; there is no real number that is the square root of a negative number If you wanted the negative square root of 144, then it is -12.
The complex conjugate of a+bi is a-bi. This is written as z* where z is a complex number. ex. z = a+bi z* = a-bi r = 3+12i r* = 3-12i s = 5-6i s* = 5+6i t = -3+7i = 7i-3 t* = -3-7i = -(3+7i)
Yes.
|5 + 12i| = +sqrt(52 + 122) = +sqrt(25 + 144) = +sqrt(169) = 13
To find the complex conjugate of a number, change the sign in front of the imaginary part. Thus, the complex conjugate of 14 + 12i is simply 14 - 12i.
It seems like your question is incomplete or unclear. If you're asking about "12i" in a mathematical or complex number context, "12i" represents a purely imaginary number where "i" is the imaginary unit (the square root of -1). If you meant something else or need further clarification, please provide more details!
The negative square root of -144 is -12i - that is -12 times the square root of minus 1, ie √-144 = 12√-1. The above is a complex number, which I suspect is not the answer you wanted; there is no real number that is the square root of a negative number If you wanted the negative square root of 144, then it is -12.
The complex conjugate of a+bi is a-bi. This is written as z* where z is a complex number. ex. z = a+bi z* = a-bi r = 3+12i r* = 3-12i s = 5-6i s* = 5+6i t = -3+7i = 7i-3 t* = -3-7i = -(3+7i)
Negative numbers have no real square roots.-144 has two square roots: 12i and -12i.
Yes.
Not necessarily, take for example the equation x^2=5-12i. Then, 3-2i satisfies the equation. However, 3+2i does not because (3+2i)^2 = 5+12i.
The multiplicative inverse of a complex number is found by taking the complex conjugate of the number and dividing by the square of its magnitude. For the complex number 3-i, the complex conjugate is 3+i. The magnitude of 3-i is sqrt(3^2 + (-1)^2) = sqrt(9 + 1) = sqrt(10). Therefore, the multiplicative inverse of 3-i is (3+i) / 10.
|5 + 12i| = +sqrt(52 + 122) = +sqrt(25 + 144) = +sqrt(169) = 13
12i=1f.
This is a complex number, not an algebraic expression. The letter i represents the imaginary unit (which is equal to sqrt(-1)). Graphiclly, with real numbers on a horizontal axis, and imaginary numbers on a vertical axis, this means starting at the origin, go to the left 5 units, and then go down 12 units.
To divide by a complex number, write it as a fraction and then multiply the numerator and denominator by the complex conjugate of the denominator - this is formed by changing the sign of the imaginary bit of the number; when a complex number (a + bi) is multiplied by its complex conjugate the result is the real number a² + b² which can be divided into the complex number of the numerator: (-4 - 3i) ÷ (4 + i) = (-4 - 3i)/(4 + i) = ( (-4 - 3i)×(4 - i) ) / ( (4 + i)×(4 - i) ) = (-16 + 4i - 12i + 3i²) / (4² + 1²) = (-16 - 8i - 3) / (16 + 1) = (-19 - 8i)/17