a) Re(iz)=-Im(z) b) Im(iz)=Re(z) c) (z+1)^2=z^2+2z+1 3. Do the following operations and simplify your answer. (1+2i)/(3-4i)+(2-i)/(5i) (5i)/((1-i)(2-i)(3-i)) c) (1-i)^3

## Step 1: Verify equations a and b### For equation , \( \Re(i z) = -\Im(z) \), if , then \( i z = i(x + yi) = -y + xi \); thus, \(\Re(i z) = -y \) and \(\Im(z) = y\). Therefore, \(\Re(i z) = -\Im(z)\) holds.### For equation , \( \Im(i z) = \Re(z) \), if , then \( i z = i(x + yi) = -y + xi \); thus, \(\Im(i z) = x \) and \(\Re(z) = x \). Therefore, \( \Im(i z) = \Re(z)\) holds.## Step 2: Verify equation c### Expand the left-hand side \((z+1)^2 = (z+1)(z+1) = z^2 + 2z +1 \). Both sides are equal, thus \((z+1)^2 = z^2 + 2z +1 \) holds.## Step 3: Simplify part (a)### Rationalize the denominators and combine fractions: ### Add the two results: ## Step 4: Simplify part (b)### Factorize the denominator and cancel as much as possible: ## Step 5: Simplify part (c)### Expand and simplify: