7
To solve this type of problem, multiply both the numerator and denominator by the conjugate of the denominator. (2 - 4i) / (4 + 2i) = (2 - 4i)(4 - 2i) / (4 + 2i)(4 - 2i) then expand all the terms, and simplify. = (8 - 20i + 8i2) / (16 - 4i2) = (8 - 20i - 8) / (16 + 4) = -20i / 20 = -i Which in the required answer format becomes, 0 + i.
3x2 + 51 = 6x Rewrite the equation so that it equates to zero 3x2 - 6x + 51 = 0 Simplify by dividing by 3 x2 - 2x + 17 = 0 Then use the quadratic formula x = {2 ± √[(-2)2 -(4x1x17)]} ÷ 2 = { 2 ± √-64} ÷ 2 = 1 ± 4i Then x = 1 + 4i and x = 1- 4i
4Σ (12 - 4i)i=0
Yes. Consider, if you can factor complex numbers, then logically, you should be able to take two complex numbers, multiply them together, and get a third. That can indeed be done. For example: (4i + 7)(3i + 2) = -12 + 8i + 21i + 14 = 29i + 2 Therefore, the complex number 29i + 2 must be divisible by 4i + 7 and 3i + 2.
(9 + 4i)^2 = 9^2 + (2)(9)(4i) +i^2 substitute i^2 for -1; = 81 + 72i -1 = 80 + 72i
-6-4i.
A product is a binary operatoin. That is, it requires two numbers to be combined. There is only one number, 2 + 4i, in the question.
To get the conjugate simply reverse the sign of the complex part. Thus conj of 7-4i is 7+4i
the problem: what is 4 + 4i + 4 + 6i what you do is add the real and imaginary parts, thus: 4+4 and 4i+6i = 8+10i answer.
When finding the conjugate of a binomial, you just reverse the sign. So the conjugate of 3+4i is 3-4i.
(x - 4i)(x + 4i) where i is the square root of -1
(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).
4i(-2 -3i) = 4i×-2 - 4i×-3i = -8i -12i² = -8i + 12 = 12 -8i → the conjugate is 12 + 8i
7
To solve this type of problem, multiply both the numerator and denominator by the conjugate of the denominator. (2 - 4i) / (4 + 2i) = (2 - 4i)(4 - 2i) / (4 + 2i)(4 - 2i) then expand all the terms, and simplify. = (8 - 20i + 8i2) / (16 - 4i2) = (8 - 20i - 8) / (16 + 4) = -20i / 20 = -i Which in the required answer format becomes, 0 + i.
Add the real and the imaginary parts separately.