express in rectangular form abi z12j3 angle 45Solutionlet 12

express in rectangular form a+bi

z=(1+2j)*(3 angle 45°)

Solution

let (1+2i)

here a=1 and b=2

modulus=sqrt(1+4)=sqrt5

arg=tan^-1(2/1)

so (1+2i)=sqrt5 (e^itan^-1 2)=sqrt5(cos tan^-1 2+i sin tan^-1 2)

z=(1+2i)(3angle 45)

=sqrt5(cos tan^-1 2+i sin tan^-1 2) (3angle 45)