The "i" in 3i means the number is imaginary.
3i where i is the square root of negative one.3i x 3i = -9
The conjugate of (84-3i) is (84+3i). This gives you a real number when multiplied.
Use the rules of division for complex numbers. Just divide 1 / (4 + 3i). This requires multiplying numerator and denominator of this fraction by (4 - 3i), to get a real number in the denominator.
0 + 3i
The "i" in 3i means the number is imaginary.
No. It is an imaginary (or complex) number.
3i where i is the square root of negative one.3i x 3i = -9
The conjugate is 7 - 3i is 7 + 3i.
[7 - 3i] To find the conjugate: the sign of the real part stays the same, and the sign of the imaginary part is reversed. So the conjugate of [7 + 3i] is [7 - 3i]
[7 - 3i] To find the conjugate: the sign of the real part stays the same, and the sign of the imaginary part is reversed. So the conjugate of [7 + 3i] is [7 - 3i]
The conjugate of (84-3i) is (84+3i). This gives you a real number when multiplied.
To form the additive inverse, negate all parts of the complex number → 8 + 3i → -8 - 3i The sum of a number and its additive inverse is 0: (8 + 3i) + (-8 - 3i) = (8 + -8) + (3 + -3)i = (8 - 8) + (3 - 3)i = 0 + 0i = 0.
3x2 + 2x + 2 = 0 Can not be factored. You can however solve it for x: 3x2 + 2x = -2 x2 + 2x/3 = -2/3 x2 + 2x/3 + 1/9 = -2/3 + 1/9 (x + 1/9)2 = -5/9 x + 1/9 = ±√(-5/9) x = -1/9 ± i√(5/9) x = -1/9 ± i√5 / 3 x = -1/9 ± 3i√5 / 9 x = (-1 ± 3i√5) / 9
- 2 - 3i
Use the rules of division for complex numbers. Just divide 1 / (4 + 3i). This requires multiplying numerator and denominator of this fraction by (4 - 3i), to get a real number in the denominator.
The answer below does find one root, and finding roots is one way to discover factors. But it does not find the complete factorization. x = -3/2 is also a root of the stated 'equation'. So two of the factors are (2x - 3) and (2x + 3). Then long division could be used to find remaining factor(s).Recall that a2 - b2 = (a + b)(a - b). Let a2 = 16x4, and b2 = 81.so, a = 4x2 and b = 9.So: 16x4 - 81 = (4x2 + 9)(4x2 - 9), and (4x2 - 9) factors to (2x + 3)(2x - 3).So the factorization is: (4x2 + 9)(2x + 3)(2x - 3).With complex: (2x + 3i)(2x - 3i)(2x + 3)(2x - 3), where i = sqrt(-1)So the other two roots are: 3i/2 and -3i/2Finding a root:16X^4 - 81 = 0add 81 to each side : 16X^4 = 81divide both sides by 16, leave as fractionX^4 = 81/16take 4th root both sidesX = 4root(81/16)this can be expressed as.........X = 4root(81)/4root(16)X = 3/2 [indicates (2x - 3) is one of the factors]check16(3/2)^4 - 81 = 016 * 81/16 - 81 = 00 = 0checks