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Question

Solve:


4+320i

A
5+2i
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B
3+5i
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C
1+5i
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D
5i2i
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Solution

The correct option is B 3+5i
Let x+iy=4+320i

(x+iy)2=4+320i

expanding ,

x2+2ixyy2=4+320i

equating real & imaginary parts

x2y2=4(1)

2xy=320(2)

By equaling the modules

(x+iy)2=4+320i

x2+y2=42+(320)2=16+180=196=14

x2+y2=14(3)

from (1)&(3),

x=±3

y=±5 - (eqn (2) demands x & y to have same sign)

ans :±(3+5i)

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