Do not use a calculator in answering this question. Find the complex numbers $z$ and $w$ which s

Question

Do not use a calculator in answering this question. Find the complex numbers $z$ and $w$ which satisfy the following simultaneous equations.$$|z| + 5w = 0$$$$iz - 4w = -4 + 7i$$Give your answers in the form of $a + ib$, where $a$ and $b$ are real constants.[5] The point $A$ on the Argand diagram represents the complex number $u$. On the copy of the Argand diagram in the Printed Answer booklet, plot the point $B$ to represent the complex number $-u$.[1] The points $C$ and $D$ represent the complex numbers $v - u$ and $(v - u)^*$ respectively, where $v$ is an unknown complex number. It is also given that $\angle CDA = 90{}^\circ $. By using the Argand diagram or otherwise, state the value of $\mathrm{Im}(v)$ and justify your answer.[2]

Accepted Answer

(a)z= 7+24i, w=-5 (b)(ii)Im(v)= 0

2025 SAJC P1 Q10

2025 SAJC P1 Q10