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To find the quotient of the complex numbers ( (4 + 4i) ) and ( (5 + 4i) ), you divide the two:
[ \frac{4 + 4i}{5 + 4i}. ]
To simplify, multiply the numerator and denominator by the conjugate of the denominator:
[ \frac{(4 + 4i)(5 - 4i)}{(5 + 4i)(5 - 4i)} = \frac{(20 - 16i + 20i - 16)}{(25 + 16)} = \frac{(4 + 4i)}{41}. ]
This results in ( \frac{4}{41} + \frac{4}{41}i ).
What else can I help you with?
Find the conjugate of 8 plus 4i.?
The conjugate of a complex number is obtained by changing the sign of its imaginary part. For the complex number (8 + 4i), the conjugate is (8 - 4i).
2 plus 4i - 7 plus 4i?
(2 + 4i) - (7 + 4i) = -5 2 + 4i - 7 + 4i = -5 + 8i
What is the sum of two complex conjugate number?
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.
What is the absolute value of 2 4i?
The absolute value of a complex number ( a + bi ) is given by the formula ( \sqrt{a^2 + b^2} ). For the complex number ( 2 + 4i ), the absolute value is calculated as follows: ( |2 + 4i| = \sqrt{2^2 + 4^2} = \sqrt{4 + 16} = \sqrt{20} = 2\sqrt{5} ). Thus, the absolute value of ( 2 + 4i ) is ( 2\sqrt{5} ).
What is the additive inverse of a complex number?
Just change the sign of both the real part, and the imaginary part. For instance, the additive inverse of:3-4i is: -3+4i (If you have the complex number in polar coordinates, add or subtract pi to the angle.)
Find the conjugate of 8 plus 4i.?
The conjugate of a complex number is obtained by changing the sign of its imaginary part. For the complex number (8 + 4i), the conjugate is (8 - 4i).
How do you factor xsquared plus 16?
(x - 4i)(x + 4i) where i is the square root of -1
What is the complex form of 4 plus 4i plus 4 plus 6i?
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.
2 plus 4i - 7 plus 4i?
(2 + 4i) - (7 + 4i) = -5 2 + 4i - 7 + 4i = -5 + 8i
What is the conjugate of -5 4i?
-9
What is the conjugate of the complex number 7-4i?
To get the conjugate simply reverse the sign of the complex part. Thus conj of 7-4i is 7+4i
Find the complex fourth root of 256i Express your answer in a plus bi form?
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
Find the absolute value of the complex number z equals 3 plus 4i?
('|x|' = Absolute value of x) |3+4i| = √(32 + 42) = √(9+16) = √25 = 5 Thus |3+4i| = 5.
What is the conjugate of -6 plus 4i?
-6-4i.
What is the conjugate of -8-4i?
The conjugate of -8-4i is -8+4i. It is obtained by changing the sign of the imaginary part of the complex number.
What is the multiplicative inverse of 4 i?
The multiplicative inverse of a complex number is found by taking the reciprocal of the number. In this case, the reciprocal of 4i is -1/4i. To find the reciprocal, you divide 1 by the complex number, which results in -1/4i. This is the multiplicative inverse of 4i.
What is the conjugate of 3 plus 4i?
When finding the conjugate of a binomial, you just reverse the sign. So the conjugate of 3+4i is 3-4i.
