Question

The modulus and amplitude of a complex number are respectively √2 and 45°.Find the complex number.​

Answer 1

Step-by-step explanation:

Polar form of complex number is

$|z| ( \cos(\theta) + i \sin(\theta) )$

Given

$|z | \: = \sqrt{2} \\ \\ \theta = 45$

Then

$complex \: \: no. \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ = \sqrt{2} ( \cos(45) + i \sin(45) ) \\ \\ = \sqrt{2} ( \frac{1}{ \sqrt{2} } + \frac{i}{ \sqrt{2} } ) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ = 1 + i \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

HENCE. COMP. NO. = 1 + i