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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.
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What is conjugate of 4i open bracket -2 -3i close bracket?
4i(-2 -3i) = 4i×-2 - 4i×-3i = -8i -12i² = -8i + 12 = 12 -8i → the conjugate is 12 + 8i
What is the answer to this -5-12i?
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.
Evaluate and express this complex number in standard form the absulote value of 5-12i?
The absolute value of a complex number is it's magnitude (distance from the origin). Think about complex numbers graphically, with reals on the horizontal axis, and imaginaries on the vertical axis. Now you have a right triangle: From the origin move to the right 5 units, then move down 12 units. The absolute value, or magnitude, is the length of the hypotenuse. For this triangle, it is 13: sqrt(5^2 + 12^2) = sqrt(25+144) = sqrt(169) = 13. For magnitudes, we are only interested in the positive square root.
How do you multiply imaginary numbers?
First, let's make sure we are not confusing imaginary numbers with complex numbers. Imaginary (sometimes called "pure imaginary" for clarity) numbers are numbers of the form ai, where a is a real number and i is the principal square root of -1. To multiply two imaginary numbers ai and bi, start by pretending that i is a variable (like x). So ai x bi = abi2. But since i is the square root of -1, i2=-1. So abi2=-ab. For example, 6i x 7i =-42. 5i x 2i =-10. (-5i) x 2i =-(-10)= 10. Complex numbers are numbers of the form a+bi, where a and b are real numbers. a is the real part, bi is the imaginary part. To multiply two complex numbers, again, just treat i as if it were a variable and then in the final answer, substitute -1 wherever you see i2. Hence (a+bi)(c+di) = ac + adi + bci + dbi2 which simplifies to ac-db + (ad+bc)i. For example: (2+3i)(4+5i) = 8 + 10i +12i + 15i2= 8 + 10i + 12i - 15 = -7 + 22i
What is the complex conjugate of a plus bi?
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)
If 3 - 2i is a solution to a polynomial equation is the complex conjugate 3 plus 2i also a solution yes or no?
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.
What is -4-3i divided by 4 plus i?
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
What is complex number of 10 12i?
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.
What is conjugate of 4i open bracket -2 -3i close bracket?
4i(-2 -3i) = 4i×-2 - 4i×-3i = -8i -12i² = -8i + 12 = 12 -8i → the conjugate is 12 + 8i
What is the absolute value of 5 plus 12i?
|5 + 12i| = +sqrt(52 + 122) = +sqrt(25 + 144) = +sqrt(169) = 13
What is the sum of (7 plus 3i) plus (8 plus 9i)?
(7 + 3i) + (8 + 9i) = (7 + 8) + (3i + 9i) = (7 + 8) + (3 + 9)i = 15 + 12i Which can also be written as: 15 + 12i = 3(5 + 4i).
What is the square root of negative 144?
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.
What is the formula of feet to inches conversion?
12i=1f.
What expression is equivalent to -12i(3-6i)?
-12i(3-6i) = -36i + 72i² = -36i + 72 × -1 = -36i - 72 = -72 - 36i = -36(2 + i)
How do you simplify 4i 3i?
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.
how to solve this 4m-12i need show the solution?
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