(9 + 4i)^2
= 9^2 + (2)(9)(4i) +i^2 substitute i^2 for -1;
= 81 + 72i -1
= 80 + 72i
(x - 4i)(x + 4i) where i is the square root of -1
To solve this problem, we first need to understand that "four times the number i" can be represented as 4i. Then, to find "12 fewer hats than 4i," we subtract 12 from 4i to get 4i - 12. Therefore, "12 fewer hats than four times the number i" is represented by the expression 4i - 12.
The four roots of 4√256 are {4, -4, 4i, and -4i}. Note that two of them are real numbers and the other two are pure imaginary, therefore 0 + 4i is the same as just 4i
7
To get the conjugate simply reverse the sign of the complex part. Thus conj of 7-4i is 7+4i
(2 + 4i) - (7 + 4i) = -5 2 + 4i - 7 + 4i = -5 + 8i
Ah, what a happy little question we have here. The number that, when squared, equals 16 is 4. Just like painting a beautiful landscape, sometimes we just need to step back and see the simple beauty in the numbers before us. Keep exploring and discovering, my friend.
-6-4i.
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
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
It's a second degree equation in 'x' that has no real solution. No real number in the place of 'x' can make that equation a true statement. There are only two "imaginary" numbers that 'x' can be: + 4i sqrt(5) - 4i sqrt(5)
It is D.
To solve this problem, we first need to understand that "four times the number i" can be represented as 4i. Then, to find "12 fewer hats than 4i," we subtract 12 from 4i to get 4i - 12. Therefore, "12 fewer hats than four times the number i" is represented by the expression 4i - 12.
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.
(3-4i)(1-i) = (3x1) + (3 x -i) + (-4i x 1) + ( -4i x -i) = 3 - 3i -4i -4 = -1 - 7i