1/(1+ 3i)
3i where i is the square root of negative one.3i x 3i = -9
4
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.
x2 + 9 = (x + 3i)(x - 3i) The answer is based on a knowledge of imaginary and complex numbers where i2 = -1
1/(1+ 3i)
3i where i is the square root of negative one.3i x 3i = -9
(3i)5 = 35 x i5 = 243 x i2 x i2 x i = 243 x (-1) x (-1) x i = 243i
(-2 + 3i) + (-1 - 2i) = -2 + 3i - 1 - 2i = -2 - 1 + 3i - 2i = -3 + i
The given term is 3√-1. Since √-1 = i, we can rewrite the term as 3i.
x2 + 9 has no real factors. Its complex factors are (x + 3i) and (x - 3i) where i is the imaginary square root of -1.
0+3i has a complex conjugate of 0-3i thus when you multiply them together (0+3i)(0-3i)= 0-9i2 i2= -1 0--9 = 0+9 =9 conjugates are used to eliminate the imaginary parts
2
3sqrt(- 1 ) = 3i --------
4
Not complex numbers (such as 4+3i), the square of these are negative because i is defined as the square root of -1
3sqrt(- 1 ) = 3i --------