-5 - 7i
the absolute value of x + iy is equal to (x^2+y^2)^.5 and is the same for the conjugate, x-iy
The easiest way to do this is treat i like a variable and multiply the binomials and combine like powers of i, then anywhere there is i², substitute it with (-1).So (4 + 3x)(3 - 4x) = {using FOIL} 4*3 - 4*4*x + 3*3*x - 3*4*x² = 12 -7x - 12x²So with x = i, you have 12 - 7i - 12*(i²) = 12 - 7i - -12 = 24 - 7iOne quick check to see if there is an error: The magnitude of the product of the two complex binomials will equal the product of the magnitude of each factor.Magnitude of a + bi = sqrt(a² + b²). The magnitudes of two numbers that are multiplied are: sqrt(4² + 3²) = 5, and sqrt(3² + (-4)²) = 5. The magnitude of the answer is sqrt(24² + (-7)²) = sqrt(576 + 49) = sqrt(625) = 25, which is 5 times 5.
1. Divide 2. Multiply (compare) 3. Subtract 4. Compare 5. Bring down 6. Start over
Start where the x and y axes cross. Go 5 units to the left on the x (horizontal axis) and then go 9 units up from there. Put a dot in that spot.
('|x|' = Absolute value of x) |3+4i| = √(32 + 42) = √(9+16) = √25 = 5 Thus |3+4i| = 5.
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)
-9
7
0 + 5i Its complex conjugate is 0 - 5i
The conjugate of a complex number is the same number (but the imaginary part has opposite sign). e.g.: A=[5i - 2] --> A*=[-5i - 2] Graphically, as you change the sign, you also change the direction of that vector. The conjugate it's used to solve operations with complex numbers. When a complex number is multiplied by its conjugate, the product is a real number. e.g.: 5/(2-i) --> then you multiply and divide by the complex conjugate (2+i) and get the following: 5(2+i)/(2-i)(2+i)=(10+5i)/5=2+i
2
For example, the conjugate of 5 + 3i is 5 - 3i. The graph of the first number is three units above the real number line; the second one is three units below the real number line.
To multiply complex numbers you can use the same FOIL rule that you use for multiplying binomials (First, Inside, Outside, Last).(4 - 3i)(5 + 2i) = (4)(5) +(4)(2i) - (3i)(5) - (3i)(2i) = 20 + 8i-15i - 6(i)^2= 20 -7i - 6(-1) = 20 + 6 -7i = 26 -7i.
No.The roots are the complex conjugate pair 5 ± 2.4495iwhere i is the imaginary square root of -1.
the absolute value of x + iy is equal to (x^2+y^2)^.5 and is the same for the conjugate, x-iy
The absolute value is sqrt(72 + 12) = sqrt(49 + 1) = sqrt(50) or 5*sqrt(2) = 7.071 approx.
[ 2 minus square root of 5 ] is the only one.