Find the modulus and argument of complex number z=(1+i)^13/(1-i) ^7 - Maths - Complex Numbers and Quadratic Equations

Question

Find the modulus and argument of complex number z=(1+i)^13/(1-i)
^7

Priyanka Kedia · Accepted Answer

Let, z=1+i131-i7         =1+i261+i1-i231-i         =1+2i+i261+i1-2i+i231-i×1+i1+i         =1+2i-161+i21-2i-131-i2         =26i61+2i+i2-23i31-i2         =-23i31+2i-11--1         =-23i32i2         =-23i4         =-8Thus, Modulus r=z=-8=8And,point -8,0 representing z=-8+0i lies on the negatve side of real axis
 Therefore, Principal Argument of z is π