Express (5+√2i/1-√2i) in the form of a + ib .

Question

Express (5+√2i/1-√2i) in the form of a + ib . (A) 1-2 √2i (B) 1-√2i (C) 1+2√2i (D) 1+√2i

Tardigrade Admin · Accepted Answer

We have, (5+√2i/1-√2i) =(5+√2i/1-√2i)×(1+√2i/1+√2i) =(5+5√2i+√2i-2/1-(√2i)2) =(3(1+2 √2i)/3) =1+2√2i

Q. Express $\frac{5 + 2 i}{1 - 2 i}$ in the form of $a + ib$ .