ABS, ARG, CONJ, RECIPROCAL

Let z=-√2-√2i where i2 = -1. Find |z|, arg(z), z* (where * indicates the complex conjugate) and (1/z). Where appropriate, write your answers in the form a + i b,
where both a and b are real numbers.
Indicate the positions of z, z* and (1/z) on an Argand diagram.

Result

a =  2
φ =  0.7854
Φ =  45 °
c = (Correct answer is: -√2+√2i) Wrong answer
d = (Correct answer is: -√2/4 + √2/4 i) Wrong answer

Step-by-step explanation:

z=22i=Re+Im i=x+y i  x=2=21.4142 y=2=21.4142  a=Re2+Im2 a=x2+y2=(1.4142)2+(1.4142)2=2
tanφ=y:x=(1.4142):(1.4142)=1=1:1 φ=arctan(y/x)=arctan((1.4142)/(1.4142))=0.7854
Φ=φ  °=φ π180   °=0.7854 π180   °=45  °=45
c=conjz=xy i c=2+2i
d=1/z d=x+i y1=x+i y1 xi yxi y d=x2y2xi y  X=x2+y2x=(1.4142)2+(1.4142)2(1.4142)0.3536 Y=x2+y2y=(1.4142)2+(1.4142)2(1.4142)0.3536  d=2/4+2/4 i



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