(2 + 4i) - (7 + 4i) = -5 2 + 4i - 7 + 4i = -5 + 8i
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 ).
-6-4i.
-9
(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
To get the conjugate simply reverse the sign of the complex part. Thus conj of 7-4i is 7+4i
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.
Add the real and the imaginary parts separately.
-4, +4, -4i and 4i