1). Find the real part of following complex numbers.
a). \((a+ib)^2\)
b). \((1+2i)(4+1i)\)
c). \((7-7i)^2\)
d). \((a+5i)(2+3i)\)
e). \((10)(2+10i)\)
f). \(\left(\displaystyle\frac{2}{3}\right)(0+2i)\)
g). \( \left( \displaystyle \frac{1}{9}+\frac{2}{3}i \right)\left(\displaystyle \frac{6}{7}+\frac{1}{8}i \right) \)
2). Find the Imaginary part of following complex numbers.
a). \((c+id)^2\)
b). \((1i+2)(4)\)
c). \((1+10i)(1+5i)\)
d). \((a+5i)(2+3i)\)
e). \((a+bi)(2+10i)\)
f). \(\left(\displaystyle\frac{1}{3}\right)(1+2i)\)
g). \( \left( \displaystyle \frac{10}{9}+\frac{8}{7}i \right)\left(\displaystyle \frac{a}{5}+\frac{a}{7}i \right) \)
Answer : 1)
a) \(a^2-b^2\) b) 2 c) 0 d) \(2a-15\) e) 20
f) 0 g) \(\displaystyle \frac{1}{84}\)
Answer : 2)
a) \(2cd\) b) 4 c) 15 d) \(3a+10\) e) \(2b+10a\)
f) \(\displaystyle \frac{2}{3}\) g) \(\displaystyle \frac{122}{315}a\)
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