For a complex number Z, if Z=(π)/41+i^4(1-√(π)i)/(√(π)+i)+(√(π)-i)/(1+√(π)i), then the value of Z/ampZ is equal to (where ampZ∈-π,π)

Question

MARKS Content Team · Accepted Answer

Correct answer: (B) 4. Z=(π)/41+i^22(1-√(π)i1+√(π)i+√(π)-i√(π)+i)/(√(π)+πi+i-√(π)) ⇒Z=(π)/41-1+2i^2(1+π+π+1)/(π+1i) ⇒Z=(π)/44-12/i=-(2π)/i=2πi ⇒Z=2π and ampZ=(π)/2 ⇒Z/ampZ=4

For a complex number $Z$ , if $Z = \frac{π}{4} {(1 + i)}^{4} (\frac{1 - \sqrt{π} i}{\sqrt{π} + i} + \frac{\sqrt{π} - i}{1 + \sqrt{π} i}),$ then the value of $(\frac{|Z|}{amp (Z)})$ is equal to (where $amp (Z) \in (- π, π]$ )

Solution

More Complex Number Questions

For a complex number Z, if Z=π41+i41-πiπ+i+π-i1+πi, then the value of ZampZ is equal to (where ampZ∈-π,π)

Solution

More Complex Number Questions

For a complex number $Z$ , if $Z = \frac{π}{4} {(1 + i)}^{4} (\frac{1 - \sqrt{π} i}{\sqrt{π} + i} + \frac{\sqrt{π} - i}{1 + \sqrt{π} i}),$ then the value of $(\frac{|Z|}{amp (Z)})$ is equal to (where $amp (Z) \in (- π, π]$ )