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COMEDK2024MathematicsComplex Number

If (1+i)²⁰⁰=2⁹⁸(a+i b) then the value of a+b is

Options

  1. A2
  2. B4
  3. C6
  4. D8

Correct answer

B. 4

Step-by-step solution

We have, (1+i)²⁰⁰ Multiply and divide by 2 aligned & [ 2 ( 1 2 + i 2 ) ]²⁰⁰= 2 ²⁰⁰ ( 1 2 + i 2 )²⁰⁰ & =2¹⁰⁰ ( 4 +i 4 )²⁰⁰ aligned aligned & (1+i)²⁰⁰=2¹⁰⁰=2⁹⁵(a+i b) & 2^2=a+i b & 4+i 0=a+i b aligned On comparing a=4, b=0 a+b=4

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