Consider a complex number 𝑧 = 𝑎 + 𝑖𝑏 where 𝑎 and 𝑏 are real. Evaluate |𝑖𝑅𝑒(𝑖𝑧) + 𝐼𝑚(𝑧)| .

Question

Need Quickk help on this question since my understanding of complex numbers isnt the best.

Consider a complex number 𝑧 = 𝑎 + 𝑖𝑏 where 𝑎 and 𝑏 are real. Evaluate |𝑖𝑅𝑒(𝑖𝑧) + 𝐼𝑚(𝑧)| .

Answer 1

z = a + ib

iz = -b + ia

Re(iz) = -b

iRe(iz) = -ib

Im(z) = b

iRe(iz) + Im(z) = b - ib

|iRe(iz) + Im(z)| = √(2b²) = b√2