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Consider the equation z2+(2+2i)z+10i−15=0, where z∈C.
Write down
the sum of the roots.
the product of the roots.
It is given that z2+(2+2i)z+10i−15=0 has a real root.
Find both roots of the equation.
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Consider the equation 5−z−3z∗=2i, where z=a+bi and a,b∈R.
Find the values of a and b.
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Consider the complex numbers w=3−4i and z=a−2ai, where a>0.
It is given that ∣wzw∗∣=5.
Show that ∣z∣=51.
Hence find the value of a.
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Find all the solutions z∈C to the equation z+z2=1.
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