Question

Express the complex number 1(1+i) in a + ib form where a and b are real. Find the value of a2+b2.

Solution

Solution: Let z = 11+i

Rationalize the given complex numberby multiplying 1 - i to mumerator and denominator

= 11+i × 1−i1−i

= 1−i1−i2 = 1−i1+1 = 1−i2

a = 12, b = −12

So, a2 + b2 = (14) + (14) = 12

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