Welcome to the world of imaginary and complex numbers.
i is defined to be a number such that i2 = -1. i is imaginary ( that is not real)
5i is i+i+i+i+i . There is no simpler form than 5i .
Please see the attached link for more about imaginary numbers.
Chat with our AI personalities
0 + 5i Its complex conjugate is 0 - 5i
The conjugate of 2 + 3i is 2 - 3i, and the conjugate of 2 - 5i is 2 + 5i.
The standard form of a complex number is a+bi. So the standard form of the negative square root of 5i is 0-√(5i).
Let a + bi be the reciprocal. So (a + bi)(2 - 5i) = 1 (a + bi)(2 - 5i) = 2a - 5ai + 2bi + 5b = (2a + 5b) + (2b - 5a)i Therefore 2a + 5b = 1 and 2b - 5a = 0. Solving the simultaneous equations, we find that a = 2/29 and b = 5/29. So the reciprocal of 2 - 5i is 2/29 + 5i/29.
9x2 + 25 has no rational factors. Its factorisation in the complex domain is:(3x + 5i)*(3x - 5i) where i is the imaginary square root of -1.