If a -2 i then which of the following is correctA- a -1- iB- a -1- iC-D- None of these

The correct option is A a=1+i We have a=√(2i) =√(2i^1/2)= √(2)[cosπ/2 + isinπ/2]^1/2 = √(2)[cosπ/4 + isinπ/4]^1/2=√(2)(1/√(2) +1/√(2)i)=1+i Trick:Check with ...

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Byju's Answer

Standard XI

Mathematics

Square Root of a Complex Number

if a =√2 i th...

Question

if a= $\sqrt[2]{2 i}$ then which of the following is correct

a=1+i

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a=1+i

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None of these

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Solution

The correct option is A
a=1+i

We have a= $\sqrt[2]{2 i}$ = $\sqrt[2]{2 i^{1 / 2}}$ = $\sqrt[2]{2}$ ${[c o s \frac{π}{2} + i s i n \frac{π}{2}]}^{1 / 2}$

= $\sqrt[2]{2}$ ${[c o s \frac{π}{4} + i s i n \frac{π}{4}]}^{1 / 2}$ = $\sqrt[2]{2}$ $(\frac{1}{\sqrt[2]{2}} + \frac{1}{\sqrt[2]{2}} i)$ =1+i

Trick:Check with options.

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if a=2√2i then which of the following is correct

The correct option is A a=1+i We have a=2√2i =2√2i1/2= 2√2[cosπ2+isinπ2]1/2 = 2√2[cosπ4+isinπ4]1/2=2√2(12√2+12√2i)=1+i Trick:Check with options.

if a= $\sqrt[2]{2 i}$ then which of the following is correct