Question

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

Answer 1

Answer:

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

Step-by-step explanation:

$\textsf{Given:}$

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

$\textsf{Multily both numerator and denominator by 2-3i}$

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

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

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

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

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

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

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

Answer 2

LOOK AT THE PICTURE⬆️⬆️⬆️

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THIS IS THE ANSWER

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