Find Im 1+i 1-2i

To find the imaginary part of the expression (1+i)/(1-2i), we first need to simplify the expression.

Step 1: Multiply the numerator and the denominator by the conjugate of the denominator. The conjugate of (1-2i) is (1+2i).

So, (1+i)(1+2i) / (1-2i)(1+2i)

Step 2: Expand the numerator and the denominator.

Numerator: 11 + 12i + i1 + i2i = 1 + 2i + i - 2 Denominator: 11 + 12i - 2i1 - 2i2i = 1 + 2i - 2i - 4

Step 3: Simplify the numerator and the denominator.

Numerator: -1 + 3i Denominator: -3

Step 4: Divide the numerator by the denominator to get the final result.

(-1 + 3i) / -3 = 1/3 - i

So, the imaginary part of the expression (1+i)/(1-2i) is -1.

To find the imaginary part of the expression (1+i)(1-2i), we first need to multiply these two complex numbers.

Step 1: Distribute (1+i) across (1-2i) = (1+i)1 + (1+i)(-2i) = 1+i -2i -2i^2

Step 2: Simplify the expression = 1 - i - 2(-1) [since i^2 = -1] = 1 - i + 2 = 3 - i

The imaginary part of the complex number is the coefficient of 'i', which is -1 in this case. So, the imaginary part of (1+i)(1-2i) is -1.