Question

Write the complex number `(2+5i)/(5+2i)` in standard form?

Answer 1

This is a division of complex numbers. We need first to transform the denominator into a real number; We do that multiplying and dividing by the complex conjugade of the denominator (`5-2i`):
`(2+5i)/(5+2i)*(5-2i)/(5-2i)=(10-4i+25i-10i^2)/(25+4)`
But `i^2=-1`
`=(10+21i+10)/29=(20+21i)/29=20/29+21/29i`
Which is in the form `a+bi`