(2 + 4i) - (7 + 4i) = -5 2 + 4i - 7 + 4i = -5 + 8i
Since the imaginary parts cancel, and the real parts are the same, the sum is twice the real part of any of the numbers. For example, (5 + 4i) + (5 - 4i) = 5 + 5 + 4i - 4i = 10.
The multiplicative inverse of a number a is a number b such that axb=1 If we look at (3-4i)/(5+2i), we see that we can multiply that by its reciprocal and the product is one. So (5+2i)/(3-4i) is the multiplicative inverse of (3-4i)/(5+2i)
(3+2i)/(5+4i)If you multiply both sides by the conjugate of the denominator (5-4i), you get:(3+2i)(5-4i)/(5+4i)(5-4i)= (23-2i)/(25 + 16 +20i - 20i)= (23-2i)/41The denominator is now real, because the i terms cancelAs a general formula (easy to expand) this would be:(a+bi)/(c+di) = [(ac+bd) + (bc-ad)i] / (c^2 + d^2)It's a very easy method, but if you're the sort of person who loves using general formulas, there it is.
The magnitude of an integer is the value of the integer with a positive (plus) sign. |5| = +5 = 5 |-5| = +5 = 5
(2 + 4i) - (7 + 4i) = -5 2 + 4i - 7 + 4i = -5 + 8i
-9
Since the imaginary parts cancel, and the real parts are the same, the sum is twice the real part of any of the numbers. For example, (5 + 4i) + (5 - 4i) = 5 + 5 + 4i - 4i = 10.
The multiplicative inverse of a number a is a number b such that axb=1 If we look at (3-4i)/(5+2i), we see that we can multiply that by its reciprocal and the product is one. So (5+2i)/(3-4i) is the multiplicative inverse of (3-4i)/(5+2i)
11
('|x|' = Absolute value of x) |3+4i| = √(32 + 42) = √(9+16) = √25 = 5 Thus |3+4i| = 5.
(3+2i)/(5+4i)If you multiply both sides by the conjugate of the denominator (5-4i), you get:(3+2i)(5-4i)/(5+4i)(5-4i)= (23-2i)/(25 + 16 +20i - 20i)= (23-2i)/41The denominator is now real, because the i terms cancelAs a general formula (easy to expand) this would be:(a+bi)/(c+di) = [(ac+bd) + (bc-ad)i] / (c^2 + d^2)It's a very easy method, but if you're the sort of person who loves using general formulas, there it is.
-6-4i.
(x - 4i)(x + 4i) where i is the square root of -1
The conjugate of -8-4i is -8+4i. It is obtained by changing the sign of the imaginary part of the complex number.
When finding the conjugate of a binomial, you just reverse the sign. So the conjugate of 3+4i is 3-4i.
4i(-2 -3i) = 4i×-2 - 4i×-3i = -8i -12i² = -8i + 12 = 12 -8i → the conjugate is 12 + 8i