Question

Express the complex number z= 5+I/2+3i in a+ib

Answer 1

$\textsf{The a+ib form of the given complex number is 1 - i}$

Step-by-step explanation:

Given:

$\mathsf{z=\frac{5+i}{2+3i}}z$$\textsf{Multily both numerator and denominator by 2-3i}$

$\mathsf{z=\frac{5+i}{2+3i}{\times}\frac{2-3i}{2-3i}}z$

$\mathsf{z=\frac{(5+i)(2-3i)}{2^2-3^2i^2}}z$

$\mathsf{z=\frac{10-15i+2i-3i^2}{4-9i^2}}z$

$\textsf{Using,}\boxed{i^2=-1}$

$\mathsf{z=\frac{10-13i-3(-1)}{4-9(-1)}}z$

$\mathsf{z=\frac{13-13i}{13}}z$

$\implies\mathsf{\bf\;z=1-i}$