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.
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
12i=1f.
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.
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.
|5 + 12i| = +sqrt(52 + 122) = +sqrt(25 + 144) = +sqrt(169) = 13
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
12i=1f.
-12i(3-6i) = -36i + 72i² = -36i + 72 × -1 = -36i - 72 = -72 - 36i = -36(2 + i)
Assume we have the product of these terms. Multiply these terms altogether to get 12i². Make note that i = √-1, i² = -1, i³ = -i and i⁴ = 1. Then, 12i² = 12(-1) = -12. That is the answer to the question.