Question: The complex number w is defined by w = 22 + 4i/(2 - i 2 ). i. Without using a calculator, show that w =

The complex number w is defined by w = 22 + 4i/(2 - i²).

i. Without using a calculator, show that w = 2 + 4i.

ii. It is given that p is a real number such that 1/4π < arg(w + p) < 3/4π. Find the set of possible values of p.

iii. The complex conjugate of w is denoted by w*. The complex numbers w and w* are represented in an Argand diagram by the points S and T respectively. Find, in the form |z − a| = k, the equation of the circle passing through S, T and the origin.

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i We have w 22 4i2 i2 22 4i2 1 since i2 1 22 4i3 223 43i Now if we multiply the numerator and denomi... View full answer

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